The angle between two vectors a and b with magnitudes `sqrt3 and 2` respectively, having `a.b=sqrt6` is

Options

A. `(pi)/(4)`
B. `(pi)/(2)`
C. `(pi)/(6)`
D. `(pi)/(3)`

Answer

A

Explanation

To determine the angle between a and b, we can use the formula `cos theta=(a.b)/(|a||b|)`
It is given that `|a|=sqrt(3), |b|=2` and `a.b =sqrt(6)`
Let `theta` be the required angle, then
`cos theta=(a.b)/(|a||b|)=sqrt(6)/(sqrt(3)xx2)=1/sqrt(2)`
`implies theta=cos^(-1) (1/sqrt(2))=cos^(-1) ("cos" pi/4)=pi/4`