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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 (

**INSTRUCTIONS:** Enter the following:

- (
**k**) Scalar - (
**V**) Vector

**Scalar Multiplication (V'):** The calculator returns the resulting vector (V') in comma separated form.

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]

**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.**(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- Vector Normal to a Plane Defined by Three Points