w=(5,12), r=(4,-5,0), and s = -(2,3,6)

(a) Find a non-zero vector v such that w v = 0.

(b) Explain what we know geometrically about the relationship between v and w.

(c) Explain why there is no such thing as w v.

2. (a) Compute r s.

(b) Without computing, explain geometrically the relationship between r s and s r.

3. (a) Let P = (7, 3, 5). Find the equation of a plane H through P with normal vector r. (

b) Find another point Q on plane H, other than P.

4. Recall the ant at the bottom left corner of a wall. The wall measures 15 feet wide and 8 feet tall. There is a speck of food exactly in the center of the wall. Refer to Figure 1. Note that the ant and wall are not drawn to scale. Assume that ant is at the origin (0, 0). Write a vector equation for the line between the ant and the food.