Question

The magnitude of two vectors are 16 and 12 units respectively and the magnitude of their scalar product is 96

Answer 1

|$\underset{A}{\rightarrow}$| = magnitude of vector A = 16 units

|$\underset{B}{\rightarrow}$| = magnitude of vector B = 12 units

θ = angle between the two vectors

$\underset{A}{\rightarrow}$.$\underset{B}{\rightarrow}$ = scaler product of the two vectors = 96

scalar product of two vectors is given as

$\underset{A}{\rightarrow}$.$\underset{B}{\rightarrow}$ = (|$\underset{A}{\rightarrow}$|) (|$\underset{B}{\rightarrow}$|) Cosθ

inserting the above values in the above equation

96 = (16) (12) Cosθ

Cosθ = 96 /( (16) (12))

Cosθ = 96 /(192)

Cosθ = 0.5

Cosθ = Cos60

θ = 60

hence the angle between the two vectors comes out to be 60 deg