Question

find the projection of u onto v. Then write u as the sum of two orthogonal vectors, one of which is proj_v u.

Answer 1

Step 1 :

Definition of vector components :

Let u and v be nonzero vectors such that

where and are orthogonal vectors.

The vector is the projection of u onto v and it is denoted by

And

Projection of u onto v :

Let u and v be non zero vectors, then the projection of u onto v is

Step 2 :

The vectors are and

The projection u onto v :

Step 3 :

Evaluation of :

The value of other orthogonal vector is

 Solution :

The projection u onto v is

The value of other orthogonal vector is