Question

the angle between vectors A and B bar is 60 what is the ratio of A . B and MOD A and B?

Answer 1

Angle between A and B bar is 60 deg.  So angle between A and B will be 120 deg.

A . B = | A | * | B  | * Cos 120  = - |A| * |B| * 1/2

The ratio [ A . B ] / [ |A| * | B | ] = -1/2

Answer 2

A.B is the dot product of two vectors.

A.B = |A | | B| cos120 ° = -|A| |B|/2

now ,
A.B/|A|.|B| = -|A|.|B|/2(|A|.|B|) = -1/2

second method :-
cos∅ = A.B/(|A|.|B|)
∅ = 120°

then ,
A.B/(|A|.|B|) = -1/2