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`vecV' = k * vecV`
Enter a value for all fields
The Vector Scalar Multiplication formula, (k⋅V), computes the vector
Vector in three dimensions which is the result of a scalar multiplication of a vector (V) and a scalar (k).
INSTRUCTIONS: Enter the following:
- (k) Scalar
- (V) Vector
Scalar Multiplication (V'): The calculator returns the resulting vector (V') in comma separated form.
The Math / Science
The formula for the scalar multiplication of a 3D vector is:
V' = k⋅V
where:
- V'[1] = k⋅V[1]
- V'[2] = k⋅V[2]
- V'[3] = k⋅V[3]
For example, if k = 2 and V = [3,6,1]
V' = [2*3, 2*6, 2*1] = [6,12,2]
3D Vector Functions
k⋅V - scalar multiplication- V/k - scalar division
- V / |V| - Computes the Unit Vector
- |V| - Computes the magnitude of a vector
- U + V - Vector addition
- U - V - Vector subtraction
- |U - V| - Distance between vector endpoints.
- |U + V| - Magnitude of vector sum.
- V • U - Computes the dot product of two vectors
- V x U - Computes the cross product of two vectors
- V x U • W - Computes the mixed product of three vectors
- Vector Angle - Computes the angle between two vectors
- Vector Area - Computes the area between two vectors
- Vector Projection - Compute the vector projection of V onto U.
- Vector Rotation - Compute the result vector after rotating around an axis.
- Vector Components 3D - Returns a vector's magnitude, unit vector, spherical coordinates, cylindrical coordinates and angle from each axis.
- (ρ, θ, φ) to (x,y,z) - Spherical to Cartesian coordinates
- (x,y,z) to (ρ, θ, φ) - Cartesian to Spherical coordinates
- (r, θ, z) to (x,y,z) - Cylindrical to Cartesian coordinates
- (x,y,z) to (r, θ, z) - Cartesian to Cylindrical coordinates
- (x,y) to (r, θ) - Cartesian to Polar
- (r, θ) to (x,y) - Polar to Cartesian
- Vector Normal to a Plane Defined by Three Points