Page 205 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

9. is a unit vector.
(a) Show that if v is any nonzero vector, then

(b) Use the result in part (a) to find a unit vector that has the same direction as the vector .
(c) Use the result in part (a) to find a unit vector that is oppositely directed to the vector .

10. in Figure Ex-10a are and .
(a) Show that the components of the vector .

(b) Let u and v be the vectors in Figure Ex-10b. Use the result in part (a) to find the components of

Figure Ex-10

Let and . Describe the set of all points (x, y, z) for which .
11.

Prove geometrically that if u and v are vectors in 2- or 3-space, then .
12.

Prove parts (a), (c), and (e) of Theorem 1 analytically.
13.

Prove parts (d), (g), and (h) of Theorem 1 analytically.
14.

For the inequality stated in Exercise 9, is it possible to have ? Explain your
15. reasoning.

16. to be equidistant from the origin
(a) What relationship must hold for the point

and the -plane? Make sure that the relationship you state is valid for positive and