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Two stage Launch vehicle, 60 kg payload to LEO
Vector-R (Vector Rapid) is a two-stage orbital expendable launch vehicle under development by the American aerospace company Vector Launch to cover the
Vector-R
Geometric object that has length and direction
physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude
Euclidean_vector
Vector of length one
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase
Unit_vector
Vector used in astronomy
In classical mechanics, the Laplace–Runge–Lenz vector (LRL vector) is a vector used chiefly to describe the shape and orientation of the orbit of one
Laplace–Runge–Lenz_vector
Vector representing the position of a point with respect to a fixed origin
In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a point P in space.
Position_(geometry)
Algebraic structure in linear algebra
operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. Real vector spaces and complex vector spaces
Vector_space
Defunct launch vehicle designer and launch service provider
Vector Launch, Inc. (formerly Vector Space Systems) was an American space technology company which aims to launch suborbital and orbital payloads. Vector
Vector_Launch
Conserved physical quantity; rotational analogue of linear momentum
represented as a pseudovector r × p, the cross product of the particle's position vector r (relative to some origin) and its momentum vector; the latter is p = mv
Angular_momentum
Calculus of vector-valued functions
primarily in three-dimensional Euclidean space, R 3 . {\displaystyle \mathbb {R} ^{3}.} The term vector calculus is sometimes used as a synonym for the
Vector_calculus
Assignment of a vector to each point in a subset of Euclidean space
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space, most commonly Euclidean space R n {\displaystyle
Vector_field
Branch of physics describing the motion of objects without considering forces
north is in the direction of the y-axis, then the coordinate vector to the base of the tower is r = (0 m, −50 m, 0 m). If the tower is 50 m high, and this
Kinematics
Direction and rate of rotation
of the angle between the vector and the x-axis. Then: d r d t = ( r ˙ cos ( φ ) − r φ ˙ sin ( φ ) , r ˙ sin ( φ ) + r φ ˙ cos ( φ ) ) , {\displaystyle
Angular_velocity
Vector field representation in 3D curvilinear coordinate systems
In vector calculus and physics, a vector field is an assignment of a vector to each point in a space. When these spaces are in (typically) three dimensions
Vector fields in cylindrical and spherical coordinates
Vector_fields_in_cylindrical_and_spherical_coordinates
Turning force around an axis
arm vectors. In symbols: τ = r × F ⟹ τ = r F ⊥ = r F sin θ {\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \implies \tau =rF_{\perp
Torque
Function valued in a vector space; typically a real or complex one
of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension
Vector-valued_function
Measure of directional electromagnetic energy flux
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or
Poynting_vector
company Vector Launch to cover the commercial small satellite launch segment (CubeSats). It was planned to be an expanded version of the Vector-R rocket
Vector-H
Mathematical function defined piecewise by polynomials
&\\P_{i-1}^{(r_{i})}(t_{i})&=P_{i}^{(r_{i})}(t_{i}).\end{aligned}}} A vector r = (r1, …, rk–1) such that the spline has smoothness C r i {\displaystyle C^{r_{i}}}
Spline_(mathematics)
Vector that points from one end of a polymer to the other
translation vectors r → i {\displaystyle {\vec {r}}_{i}} connect between these points. The end-to-end vector R → {\displaystyle {\vec {R}}} is the sum
End-to-end_vector
Fourier transform of a real-space lattice, important in solid-state physics
{k} \cdot \mathbf {r} +\varphi )} at a fixed time t {\displaystyle t} , where r {\displaystyle \mathbf {r} } is the position vector of a point in real
Reciprocal_lattice
Four-dimensional number system
represent vectors in 3D space, then it turns out that the reflection of a vector r in a plane perpendicular to a unit vector w can be written: r ′ = − w r w
Quaternion
Celestial orbit whose trajectory is a conic section in the orbital plane
vector function r {\displaystyle \mathbf {r} } and its derivatives can now be rewritten as: r = r ( cos θ x ^ + sin θ y ^ ) = r r ^ r ˙ = r ˙ r ^
Kepler_orbit
Class of problems in classical mechanics
r ) r ^ {\displaystyle \mathbf {F} =F(r){\hat {\mathbf {r} }}} where r is the vector magnitude |r| (the distance to the center of force) and r̂ = r/r
Classical central-force problem
Classical_central-force_problem
Definite integral of a scalar or vector field along a path
d t . {\displaystyle I=\int _{a}^{b}f(\mathbf {r} (t))\left|\mathbf {r} '(t)\right|dt.} For a vector field F: U ⊆ Rn → Rn, the line integral along a
Line_integral
Cartesian vectors of position and velocity of an orbiting body in space
the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position ( r {\displaystyle \mathbf {r} } ) and velocity (
Orbital_state_vectors
Computer graphics images defined by points, lines and curves
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as
Vector_graphics
position vector. When multiplied by a time difference, it results in the angular displacement tensor. A vector r {\displaystyle \mathbf {r} } undergoing
Angular_velocity_tensor
Formulas in differential geometry
{R} ^{3},} and are defined as follows: T is the unit vector tangent to the curve, pointing in the direction of motion. N is the normal unit vector, the
Frenet–Serret_formulas
Mathematical parametrization of vector spaces by another space
In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space
Vector_bundle
Mathematical operation on vectors in 3D space
product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional
Cross_product
Problem in celestial mechanics
position vectors r 1 = r 1 r ^ 1 , r 2 = r 2 r ^ 2 {\displaystyle \mathbf {r} _{1}=r_{1}{\hat {\mathbf {r} }}_{1},\,\mathbf {r} _{2}=r_{2}{\hat {\mathbf {r} }}_{2}}
Lambert's_problem
Vector space with a notion of nearness
A topological vector space is a vector space that is also a topological space with the property that the vector space operations (vector addition and scalar
Topological_vector_space
Quantity in electromagnetism
In classical electromagnetism, magnetic vector potential (often denoted A) is the vector quantity defined so that its curl is equal to the magnetic field
Magnetic_vector_potential
Physical quantity that is a vector
the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity
Vector_quantity
Special mathematical functions defined on the surface of a sphere
{1}{r_{1}}}+P_{1}(\cos \gamma ){\frac {r}{r_{1}^{2}}}+P_{2}(\cos \gamma ){\frac {r^{2}}{r_{1}^{3}}}+\cdots } where γ is the angle between the vectors x
Spherical_harmonics
Mechanical force towards or away from a point
of force. F ( r ) = F ( r ) r ^ {\displaystyle \mathbf {F} (\mathbf {r} )=F(\mathbf {r} ){\hat {\mathbf {r} }}} where F is a force vector, F is a scalar
Central_force
Equation in analytic geometry
and point-line distance). It is written in vector notation as r → ⋅ n → 0 − d = 0. {\displaystyle {\vec {r}}\cdot {\vec {n}}_{0}-d=0.\,} The dot ⋅ {\displaystyle
Hesse_normal_form
Vector field that is the gradient of some function
In vector calculus, a conservative vector field is a vector field that is the gradient of some function. A conservative vector field has the property
Conservative_vector_field
Multivariate derivative (mathematics)
In vector calculus, the gradient of a scalar-valued differentiable function f {\displaystyle f} of several variables is the vector field (or vector-valued
Gradient
Use of coordinates for representing vectors
Vector notation In mathematics and physics, vector notation is a commonly used notation for representing vectors, which may be Euclidean vectors, or more
Vector_notation
Method of data analysis
matrix. r = a random vector of length p r = r / norm(r) do c times: s = 0 (a vector of length p) for each row x in X s = s + (x ⋅ r) x λ = rTs // λ is
Principal_component_analysis
Force directed to the center of rotation
base of Δ r {\displaystyle \Delta {\textbf {r}}} (position vector difference) and a leg length of r {\displaystyle r} | Δ v | v = | Δ r | r {\displaystyle
Centripetal_force
Vector space on which a distance is defined
{\displaystyle V} is a vector space over K {\displaystyle K} , where K {\displaystyle K} is a field equal to R {\displaystyle \mathbb {R} } or to C {\displaystyle
Normed_vector_space
Set of methods for supervised statistical learning
In machine learning, a support vector machine (SVM) or support vector network is a supervised max-margin model with associated learning algorithms that
Support_vector_machine
Formulation of physics
Euclidean space. Let r 1 , … , r N {\displaystyle \displaystyle \mathbf {r} _{1},\,\ldots ,\,\mathbf {r} _{N}} be their radius-vectors in some inertial coordinate
Newtonian_dynamics
Broad concept generalizing scalars in mathematics and physics
In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Laws describing planetary orbits
position vector twice to obtain the velocity vector and the acceleration vector: r ˙ = r ˙ r ^ + r r ^ ˙ = r ˙ r ^ + r θ ˙ θ ^ , r ¨ = ( r ¨ r ^ + r ˙ r ^ ˙
Kepler's laws of planetary motion
Kepler's_laws_of_planetary_motion
Demographic measure
rich vector r {\displaystyle \mathbf {r} } and the poor vector p {\displaystyle \mathbf {p} } : r ^ = r | r | 1 = r R {\displaystyle {\hat {\mathbf {r} }}={\frac
Index_of_dissimilarity
Frame of reference for an orbit
and velocity vectors can be determined for any location of the orbit. The position vector, r, can be expressed as: r = r cos θ p ^ + r sin θ q ^ {\displaystyle
Perifocal_coordinate_system
Set of vectors used to define coordinates
frames of reference. A basis B of a vector space V over a field F (such as the real numbers R {\displaystyle \mathbb {R} } or the complex numbers C {\displaystyle
Basis_(linear_algebra)
can be written as the sum of several r-vectors. Some r-vectors are scalars (r = 0), vectors (r = 1) and bivectors (r = 2). One may generate a finite-dimensional
Universal_geometric_algebra
Sports car produced from 1990 to 1993, based on the Vector W2
The Vector W8 is a sports car produced by American automobile manufacturer Vector Aeromotive Corporation from 1989 to 1993. It was designed by company
Vector_W8
Velocity of an object as the rate of distance change between the object and a point
position vector r ^ = r / r {\displaystyle {\hat {r}}=\mathbf {r} /{r}} (or LOS direction), the range rate is simply expressed as r ˙ = ⟨ r , v ⟩ r = ⟨ r ^
Radial_velocity
Parameter of Keplerian orbits
{\left|r\right|} }}} (if r ⋅ v < 0 then replace ν by 2π − ν) where: v is the orbital velocity vector of the orbiting body, e is the eccentricity vector, r is
True_anomaly
Graphics mode on the Super NES video game console
define the vector r 0 {\displaystyle \mathbf {r} _{0}} , the origin). Specifically, 2D screen coordinate vector r {\displaystyle \mathbf {r} } is translated
Mode_7
Region of space in which a force acts
M r 2 r ^ {\displaystyle \mathbf {g} ={\frac {-GM}{r^{2}}}{\hat {\mathbf {r} }}} , where the radial unit vector r ^ {\displaystyle {\hat {\mathbf {r} }}}
Force_field_(physics)
Physical spaces representing position and momentum, Fourier-transform duals
all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point
Position_and_momentum_spaces
Measurable property of a material or system
vector norm). For example, let Z {\displaystyle Z} be "2 metres"; then, { Z } = 2 {\displaystyle \{Z\}=2} is the numerical value and [ Z ] = m e t r e
Physical_quantity
Mathematical identities
following are important identities involving derivatives and integrals in vector calculus. For a function f ( x , y , z ) {\displaystyle f(x,y,z)} in three-dimensional
Vector_calculus_identities
Number of vectors in any basis of the vector space
written as dim ( V ) {\displaystyle \dim(V)} instead. The vector space R 3 {\displaystyle \mathbb {R} ^{3}} has { ( 1 0 0 ) , ( 0 1 0 ) , ( 0 0 1 ) } {\displaystyle
Dimension_(vector_space)
Vector in relativity
In special relativity, a four-vector (or 4-vector, sometimes Lorentz vector) is an element of a four-dimensional vector space object with four components
Four-vector
Vector quantity in celestial mechanics
the relative position vector r {\displaystyle \mathbf {r} } and the relative velocity vector v {\displaystyle \mathbf {v} } . h = r × v = L m {\displaystyle
Specific_angular_momentum
Length in a vector space
In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance
Norm_(mathematics)
Random variable with multiple component dimensions
probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either
Multivariate_random_variable
Simulation of a dynamical system of particles
Vector3 r_unit_vector = { r_vector.e[0] / r_mag, r_vector.e[1] / r_mag, r_vector.e[2] / r_mag }; a_g.e[0] += acceleration * r_unit_vector.e[0]; a_g.e[1]
N-body_simulation
Memory unit used in neural networks
, the output vector is h 0 = 0 {\displaystyle h_{0}=0} . z t = σ ( W z x t + U z h t − 1 + b z ) r t = σ ( W r x t + U r h t − 1 + b r ) h ^ t = ϕ (
Gated_recurrent_unit
Radiance of a surface
as I ( x , t ; r 1 , ν ) {\displaystyle I(\mathbf {x} ,t;\mathbf {r} _{1},\nu )} where: ν denotes frequency. r1 denotes a unit vector, with the direction
Spectral_radiance
Coordinate system whose directions vary in space
natural basis vectors: h 1 = ∂ r ∂ q 1 ; h 2 = ∂ r ∂ q 2 ; h 3 = ∂ r ∂ q 3 . {\displaystyle \mathbf {h} _{1}={\dfrac {\partial \mathbf {r} }{\partial q^{1}}};\;\mathbf
Curvilinear_coordinates
Circulation density in a vector field
In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional
Curl_(mathematics)
Coefficients in a series expansion of a potential
the vector r ′ {\displaystyle \mathbf {r} '} has coordinates ( r ′ , θ ′ , ϕ ′ ) {\displaystyle (r',\theta ',\phi ')} where r ′ {\displaystyle r'} is
Spherical_multipole_moments
Algebraic operation on coordinate vectors
numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry, the scalar product of two vectors is the dot product of their
Dot_product
Shading algorithm in computer graphics
{\text{d}}}+k_{\text{s}}({\hat {R}}_{m}\cdot {\hat {V}})^{\alpha }i_{m,{\text{s}}}).} where the direction vector R ^ m {\displaystyle {\hat {R}}_{m}} is calculated
Phong_reflection_model
Decomposition of periodic functions
( r ) = f ( R + r ) {\displaystyle f(\mathbf {r} )=f(\mathbf {R} +\mathbf {r} )} for any lattice vector R {\displaystyle \mathbf {R} } . This situation
Fourier_series
Mathematical function
an R {\displaystyle \mathbb {R} } -algebra, such as the complex numbers or the quaternions. The structure R {\displaystyle \mathbb {R} } -vector space
Function_of_a_real_variable
Extension of the scalar spherical harmonics for use with vector fields
{r} }}} being the unit vector along the radial direction in spherical coordinates and r {\displaystyle \mathbf {r} } the vector along the radial direction
Vector_spherical_harmonics
Concept in the physics of electromagnetism
In electromagnetism, the magnetic moment or magnetic dipole moment is a vector quantity which characterizes the strength and orientation of a magnet or
Magnetic_moment
Physical quantity that changes sign with improper rotation
physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under continuous rigid transformations such as rotations
Pseudovector
Index of articles associated with the same name
In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:
Vector_multiplication
Simple quantum mechanical system
+ r ⋅ σ . {\displaystyle \mathbf {H} =\alpha \cdot \sigma _{0}+\mathbf {r} \cdot {\boldsymbol {\sigma }}.} The vector r {\displaystyle \mathbf {r} }
Two-state_quantum_system
Motion problem in classical mechanics
where r = |r| and r̂ = r/r is the corresponding unit vector. We now have: μ r ¨ = F ( r ) r ^ , {\displaystyle \mu {\ddot {\mathbf {r} }}={F}(r){\hat {\mathbf
Two-body_problem
Vector on which a quadratic form is zero
In mathematics, given a vector space X with an associated quadratic form q, written (X, q), a null vector or isotropic vector is a non-zero element x
Null_vector
Law of classical electromagnetism
while the fundamental vector here is H. The Biot–Savart law is used for computing the resultant magnetic flux density B at position r in 3D-space generated
Biot–Savart_law
Vector describing a wave; often its propagation direction
In physics, a wave vector (or wavevector) is a vector used in describing a wave, with a typical unit being cycle per metre. It has a magnitude and direction
Wave_vector
Agent that carries and transmits pathogens
In epidemiology, a disease vector is any living agent that carries and transmits an infectious pathogen such as a parasite or microbe, to another living
Disease_vector
Vector sum of all forces acting upon a particle or body
torque vector, and τ = F k {\displaystyle \ \tau =Fk} is the amount of torque. The vector r {\displaystyle \mathbf {r} } is the position vector of the
Net_force
Object movement along a circular path
{\displaystyle \mathbf {r} } is the radial vector from the origin to the particle location: r ( t ) = R u ^ R ( t ) , {\displaystyle \mathbf {r} (t)=R{\hat {\mathbf
Circular_motion
Ways to represent 3D rotations
velocity vector and the angular velocity vector is d r d t = ω ( t ) × r ( t ) = [ ω ] × r ( t ) {\displaystyle {\frac {\mathrm {d} \mathbf {r} }{\mathrm
Rotation formulations in three dimensions
Rotation_formulations_in_three_dimensions
Mathematical concept
\alpha } , the Reeb vector field satisfies R ∈ k e r d α , α ( R ) = 1 {\displaystyle R\in \mathrm {ker} \ d\alpha ,\ \alpha (R)=1} , in particular
Reeb_vector_field
Coordinates comprising a distance and an angle
this vector equation becomes: F r + m r Ω 2 = m r ¨ F φ − 2 m r ˙ Ω = m r φ ¨ , {\displaystyle {\begin{aligned}F_{r}+mr\Omega ^{2}&=m{\ddot {r}}\\F_{\varphi
Polar_coordinate_system
Rate of change of velocity
Like velocity, acceleration has a magnitude and a direction, making it a vector quantity. The SI unit for acceleration is metre per second squared (m⋅s−2
Acceleration
Influence that can change motion of an object
}}{{R_{\oplus }}^{2}}}{\hat {\mathbf {r} }},} where the vector direction is given by r ^ {\displaystyle {\hat {\mathbf {r} }}} , is the unit vector directed
Force
Equations that describe the behavior of a physical system
described by a vector field of resistive forces R = R(r, t), − G m M | r | 2 e ^ r + R = m d 2 r d t 2 + 0 ⇒ d 2 r d t 2 = − G M | r | 2 e ^ r + A {\displaystyle
Equations_of_motion
Propagation delay of EM radiation (light)
the EM field is radiated at position vector r′ (within the source charge distribution), and an observer at position r measures the EM field at time t, the
Retarded_time
Numerical method used in structural mechanics
\mathbf {k} ^{e}} . r {\displaystyle \mathbf {r} } = vector of the system's nodal displacements. R o {\displaystyle \mathbf {R} ^{o}} = vector of equivalent
Finite element method in structural mechanics
Finite_element_method_in_structural_mechanics
Set of coordinates used in few-body calculations
m_{k}\ .} The vector r N {\displaystyle {\boldsymbol {r}}_{N}} is the center of mass of all the bodies and r 1 {\displaystyle {\boldsymbol {r}}_{1}} is the
Jacobi_coordinates
Algebraic structure designed for geometry
such as vectors. Geometric algebra is built out of two fundamental operations, addition and the geometric product. Multiplication of vectors results in
Geometric_algebra
Matrix representing a Euclidean rotation
coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: R v = [ cos θ − sin θ sin θ cos θ ] [ x y ] = x
Rotation_matrix
Mathematical measure of how much a curve or surface deviates from flatness
Both γ and –γ trace the same path in R n {\displaystyle \mathbb {R} ^{n}} and so have the same curvature vector and curvature at each point P on the curve
Curvature
Damping of electric fields
r | 2 r ^ , {\displaystyle \mathbf {F} ={\frac {q_{1}q_{2}}{4\pi \varepsilon \left|\mathbf {r} \right|^{2}}}{\hat {\mathbf {r} }},} where the vector r
Electric-field_screening
Vector space equipped with a bilinear product
mathematics, an algebra over a field (often simply called an algebra) is a vector space equipped with a bilinear product. Thus, an algebra is an algebraic
Algebra_over_a_field
VECTOR R
VECTOR R
VECTOR R
VECTOR R
VECTOR R
VECTOR R
VECTOR R
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VECTOR R