Higher Engineering Mathematics, Sixth Edition

264 Higher Engineering Mathematics

(a)−r (b) 3p (c) 2p+ 3 q (d)−p+ 2 r

(e) 0. 2 p+ 0. 6 q− 3. 2 r

(a) −r=−(− 3 i+ 5 j− 4 k)=+ 3 i− 5 j+ 4 k

(b) 3p= 3 ( 3 i+ 2 k)= 9 i+ 6 k

(c) 2p+ 3 q= 2 ( 3 i+ 2 k)+ 3 ( 4 i− 2 j+ 3 k)

= 6 i+ 4 k+ 12 i− 6 j+ 9 k

= 18 i− 6 j+ 13 k

(d) −p+ 2 r=−( 3 i+ 2 k)+ 2 (− 3 i+ 5 j− 4 k)

=− 3 i− 2 k+(− 6 i+ 10 j− 8 k)

=− 3 i− 2 k− 6 i+ 10 j− 8 k

=− 9 i+ 10 j− 10 k

(e) 0. 2 p+ 0. 6 q− 3. 2 r= 0. 2 ( 3 i+ 2 k)

+ 0. 6 ( 4 i− 2 j+ 3 k)− 3. 2 (− 3 i+ 5 j− 4 k)

= 0. 6 i+ 0. 4 k+ 2. 4 i− 1. 2 j+ 1. 8 k

+ 9. 6 i− 16 j+ 12. 8 k

= 12. 6 i− 17. 2 j+ 15 k

Now try the following exercise

Exercise 106 Further problems oni,j,k

notation

Given thatp= 2 i+ 0. 5 j− 3 k,q=−i+j+ 4 k

andr= 6 j− 5 k, evaluateand simplifythefollow-

ing vectors ini,j,kform:

1.−q [i−j− 4 k]

2. 2p [4i+j− 6 k]
   3.q+r [−i+ 7 j−k]
   4.−q+ 2 p [5i− 10 k]


3. 3q+ 4 r [− 3 i+ 27 j− 8 k]
   6.q− 2 p [− 5 i+ 10 k]


4. p+q+r [i+ 7. 5 j− 4 k]


5. p+ 2 q+ 3 r [20. 5 j− 10 k]


6. 2 p+ 0. 4 q+ 0. 5 r [3. 6 i+ 4. 4 j− 6. 9 k]


7. 7r− 2 q [2i+ 40 j− 43 k]