# 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**

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