urgent pls help hw

Question

Find the vector projection of v onto w.

v= < 2,6 > ; w= < 3,3>

Answer 1

The (orthogonal) projection of v onto w is given by the scalar

[(v . w)/(v . w)]

multiplied by the vector w. Here the . is the vector dot product. In this case:

1. v . w = 2*3 + 6*3 = 24
2. w . w = 3*3 + 3*3 = 18

Thus the projection is (24/18) w = <4, 4>.

You can always check your work by computing v - (proj) and verifying that the dot product with (proj) is zero.