If a and b are unit vectors where (3a-b) dot (a + 2b) = 4, find the acute angle between a and b.

Expert Answers
justaguide eNotes educator| Certified Educator

The angle between two vectors A and B is arc cos[(A dot B)/|A||B|]

Here A = (3a - b) and B = (a + 2b)

A dot B = 4

=> (3a - b) dot (a + 2b) = 4

=> 3a dot a - b dot a + 3a dot 2b - b dot 2b = 4

=> 3 - b dot a + 6(a dot b) - 2 = 4

=> 5(a dot b) = 3

=> a dot b = 3/5

a dot b = |a|*|b|*cos x = 3/5, where x is the acute angle between a and b

=> cos x = 3/5 as |a| = |b| = 1

x = arc cos (3/5)

x = 53.13 degrees.

The acute angle between a and b is 53.13 degrees.