Question

How do you find the projection of u=<62,21> onto v=<-12,4>?

Answer 1

`x * hat v` below

Explanation:

Scalar product: `u * v = |u| * |v| * cos theta`

But the projection is the `hat v` multiplied by the scalar horizontal leg: `cos theta = x/|u|`

Therefore `x hat v = |u| * cos theta * v/|v| = |u| * frac{(u * v)}{|u| * |v|} * v/|v|`

`(u * v) = - 62 * 12 + 21* 4 = -660`

`(v * v) = 12^2 + 4^2 = 160`

`x hat v = -660/160 * (-12,4) = (99/2, -33/2)`