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

The dot product of (3a - 2b) and (a + 2b) is
4

a dot b = |a||b|cos x, where x is the angle between the
two vectors.

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

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

=> 3|a|^2 + 6a dot b - 2 b dot a - 4|b|^2 =
4

as a and b are unit vectors |a| = |b| =
1

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

=> 4*(a dot b) =
5

=> a dot b = 5/4

But
as a and b are unit vectors a dot b <
1.

It is not possible for (3a - 2b) dot
(a+2b) to be equal to 4.