If |a| = 4, |b| = 2 and the angle between a and b is π/6

If |a| = 4, |b| = 2 and the angle between a and b is π/6, then (a × b)2 is equal to

  1. 14
  2. 16
  3. 36
  4. 48

Solution

Using fact that (a × b)2 = a2b2 - (a.b)2

= a2b2 - a2b2 cos2 θ

= a2b2(1 - cos2 θ)

= a2b2 sin2 θ

= 16 × 4 × 1/4 = 16

The correct option is B.