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

1 Answer

Answer:

#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)#