264 Higher Engineering Mathematics
(a) −r (b) 3p (c) 2p + 3q (d) −p + 2r
(e) 0.2p + 0.6q − 3.2r
(a) −r = −(−3i + 5j − 4k) = +3i − 5j + 4k
(b) 3p = 3(3i + 2k) = 9i + 6k
(c) 2p + 3q = 2(3i + 2k) + 3(4i − 2j + 3k)
= 6i + 4k + 12i − 6j + 9k
= 18i − 6j + 13k
(d) −p + 2r = −(3i + 2k) + 2(−3i + 5j − 4k)
= −3i − 2k + (−6i + 10j − 8k)
= −3i − 2k − 6i + 10j − 8k
= −9i + 10j − 10k
(e) 0.2p + 0.6q − 3.2r = 0.2(3i + 2k)
+0.6(4i − 2j + 3k) − 3.2(−3i + 5j − 4k)
= 0.6i + 0.4k + 2.4i − 1.2j + 1.8k
+9.6i − 16j + 12.8k
= 12.6i − 17.2j + 15k
Now try the following exercise
Exercise 106 Further problems on i, j , k
notation
Given that p = 2i + 0.5j − 3k, q = −i + j + 4k
and r = 6j − 5k, evaluate and simplify the following vectors in i, j , k form:
1. −q
[i − j − 4k]
2. 2p
[4i + j − 6k]
3. q + r
[−i + 7j − k]
4. −q + 2p
[5i − 10k]
5. 3q + 4r
[−3i + 27j − 8k]
6. q − 2 p
[−5i + 10k]
7. p + q + r
[i + 7.5j − 4k]
8. p + 2q + 3r
[20.5j − 10k]
9. 2p + 0.4q + 0.5r [3.6i + 4.4j − 6.9k]
10. 7r − 2q
[2i + 40j − 43k]