Revision: Vectors Exercises

1. If a = (2,1, 2), b = (1, 2, 1) and c = (1,2, 1), find

(a) a + b + c

(b) a.b

(c) b.c

(d) a.c

(e) a a

(f) a b

(g) b c

(h) |a|

(i) the unit vectors in the directions of a and b.

2. Which of the following vectors are parallel and which are perpendicu-lar?

p = 2i j, q = 4i 2j, r = 2i + 4j.

3. If e = (5t2, cos t, sin2 t), find dedt

.

1

Vectors: Solutions

1. (a) (2,-1,4)

(b) -2

(c) -4

(d) 6

(e) 0

(f) (-5,-4,3)

(g) (4,2,0)

(h) 3

(i) a = 13(2,1, 2), b = 1

6(1, 2, 1).

2. p and q are parallel; p and r are perpendicular; q and r are perpen-dicular.

3. dedt

= (10t, sin t, 2 sin t cos t).

2