Vector Projection

Trigonometry

sin Θ = p/h, cos Θ = b/h, tan Θ = p/b where p: perpendicular, h: hypotenuse, b:base

Vector projection for the indicated red vector is read as the vector projection of v onto u. (Imagine projecting a long light beam parallel to v which casts a shadow onto u)

Finding Scalar Projection

Scalar projection is the scalar value of the red line without taking direction into consideration.

$$cosθ = \frac{ScalarProjection} {|v|}$$

After solving the mathematical equations:

$$Scalar Projection = \frac{u⋅v}{ |u|}$$

$$Vector Projection = (\frac{u⋅v}{ |u|}) \frac{u}{ |u|}$$

Note: Vector Projection is simply a product of multiplying scalar projection with a unit vector u in the same direction as u. u.v: vector dot product |u|: length(norm) of u

Link: https://en.m.wikipedia.org/wiki/Vector_projection