# Vector Projection

### Scalar Projection

### Vector Projection

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

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

#### Examples

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

Calculate the vector projection of on the vector .

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

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.

= (-3, 5) = (3, -5)

= (-7, -1) = (7, 1)

= (-4, -6) = (4, 6)

· = |(−3)· (−7) + 5 · (-1)| = 16

· = 7· 4 + 1 · 6 = 34