- (i) − 5 i− 5 j+ 7 k,
1
3√
11(− 5 i− 5 j+ 7 k)(ii) 2i+ 31 j+ 13 k,1
√
1134( 2 i+ 31 j+ 13 k)(iii) 7i+ 11 j− 8 k,1
√
234( 7 i+ 11 j− 8 k)(iv) − 9 i+ 3 j+ 3 k,1
√
11(− 3 i+j+k)(v) −i− 7 j+ 3 k,1
√
59(−i− 7 j+ 3 k)(vi) 3i− 3 j+ 3 k,1
√
3(i−j+k)25.(i) i−j+ 2 k (ii) −k (iii) 21i− 21 j
- (i) a·b×c=−23, a·c×b=23, b·a×b= 0
(ii) a×(b×c)=− 3 i−j+ 7 k, (a×b)×c=i+j+k,
b×(b×a)=− 7 i+ 8 j−k- (i)
d
dt(f·g)= 3 t^2 +(t^2 + 2 t)et+2costd
dt(f×g)=( 2 et− 2 tsint−t^2 cost)i−( 4 t−sint−tcost)j+( 4 t^3 −et−tet)k(ii)d
dt(f·g)=5cos2t− 2 tsin 2t− 18 td
dt(f×g)=−( 6 tsin 2t+ 6 t^2 cos 2t)i+( 3 − 6 t^2 sin 2t+ 6 tcos 2t)j−(5sin2t+ 2 tcos 2t)k