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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 = (5t 2 , cos t, sin 2 t), find de dt . 1

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  • 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


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