Chapter 7.5, Problem 51PE

Given $v=〈-3,6〉$ and $w=〈1,3〉$ ,

a. Find ${\text{proj}}_{w}v$ . (See Example 4)

b. Find vectors $v_1$ and $v_2$ such that $v_1$ , is parallel to w, $v_2$ is orthogonal to w, and $v_1+v_2=v$ .

c. Using the results from part (b) show that $v_1$ is parallel to w by finding a constant c such that $v_1=cw$ .

d. Show that $v_2$ is orthogonal to w.

e. Show that $v_1+v_2=v$ .