Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b

Let a and b be two unit vectors. If the vectors c = a + 2b and d = 5a - 4b are perpendicular to each other, then the angle between a and b is

  1. π/4
  2. π/6
  3. π/2
  4. π/3

Solution

c.d = 0

5a2 + 6a.b - 8b2 = 0

6a.b = 3

a.b = 1/2

The correct option is D.