Vectors 2 Question 5

5. Let a=3i^+2j^+xk^ and b=i^j^+k^, for some real x. Then |a×b|=r is possible if

(2019 Main, 8 April II)

(a) 0<r32

(b) 32<r332

(c) 332<r<532

(d) r532

Show Answer

Answer:

Correct Answer: 5. (d)

Solution:

  1. Given vectors are a=3i^+2j^+xk^

and b=i^j^+k^

a×b=|i^j^k^32x111|=i^(2+x)j^(3x)+k^(32)=(x+2)i^+(x3)j^5k^|a×b|=(x+2)2+(x3)2+25=2x22x+4+9+25=2(x2x+14)12+38=2(x12)2+752

=2(x2x+14)12+38=2(x12)2+752

So, |a×b|752 [at x=12,|a×b| is minimum]

r532



NCERT Chapter Video Solution

Dual Pane