Let and be three vectors. Find the values of x for which the angle between and is acute and the angle between and is obtuse

We know that,

Where, x is the angle between two vectors

Applying for

Since angle between is acute cos x should be greater than 0

x² – 4 > 0

x > 2 and x < –2

applying for

Since angle between is obtuse cos x should be less than

0

x² – 9 < 0

x > –3 and x < 3