52. Given v = (4,-3) and w = (2,-2).
a. Find proj<sub>w</sub> v.
b. Find vectors v<sub>1</sub> and v<sub>2</sub> such that v<sub>1</sub> is parallel to w, v<sub>2</sub> is orthogonal to w, and v<sub>1</sub> + v<sub>2</sub> = v.
c. Using the results from part (b) show that v<sub>1</sub> is parallel to w by finding a constant c such that v<sub>1</sub> = cw.
d. Show that v<sub>2</sub> is orthogonal to w.
e. Show that v<sub>1</sub> + v<sub>2</sub> = v.