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`W = V " onto " U`

Enter a value for all fields

The **Vector Projection** calculator computes the resulting vector (**W**) that is a projection of vector **V** onto vector **U** in three dimensional space.* Vector V projected on vector U*

**INSTRUCTIONS:** Enter the following:

- (
**V**): Enter the x, y and z components of**V**separated by commas (e.g. 3,4,2) - (
**U**): Enter the x, y and z components of**U**separated by commas (e.g. 3,4,2)

**Vector Projection (W):** The calculator returns the vector in comma separated form.

To compute the projection of vector V onto vector U:

- Compute the magnitude of vector V
- Compute angle between vectors V and U
- Compute the unit vector of vector U
- Compute the scalar (k) associated with the projection which is the magnitude of V times the cosine of the angle between them.
- Compute the vector resulting in the scalar multiplication of the unit vector of U and the scalar (k).

**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