Vector Projection

Scalar Projection

Scalar Projection

Scalar Projection Formula

Scalar Projection Formula

Vector Projection

The vector projection is the unit vector of Vector by the scalar projection of u on v.

Vector Projection Formula

The scalar projection of u on v is the magnitude of the vector projection of u on v.


Examples

Calculate the vector projection of Vector = (2, 1) on the vector Vector = (−3, 4).

Vector Projection Example


Calculate the vector projection of Vector on the vector Vector.

Vector Projection Example

Vector Projection Calculations

Vector Projection Solution


Calculate the scalar projection of the vector Vector on the vector Vector if: A = (6,0), B = (3,5) and C = (−1,−1).

Scalar Projection

Scalar Projection Example

Scalar Projection Calculations

Scalar Projection Solution

 


If the vertices of a triangle are A = (6, 0), B = (3, 5) and C = (−1, −1), compute the scalar projections of the sides AB and CB on AC, and check that their sum is equal to the length of AC.

Scalar Projection

Vector = (-3, 5) Vector = (3, -5)Scalar Projection Calculations

Vector = (-7, -1) Vector = (7, 1) Scalar Projection Calculations

Vector = (-4, -6) Vector = (4, 6) Scalar Projection Calculations

Vector  · Vector = |(−3)· (−7) + 5 · (-1)| = 16

Vector · Vector = 7· 4 + 1 · 6 = 34

Scalar Projection Calculations

Scalar Projection Calculations

Scalar Projection Solution