If a + b + c = 0 and |a| = 1, |b| = 1, |c| =` sqrt3` ,then the angle between a and b is

Options

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

Answer

B

Explanation

We have ,
` a+ b+c =0 and |a| =1, |b| =1 , |c| =sqrt3`
Now , a+b+c=0
` Rightarrow a+b =-c `
` Rightarrow |a+b|^(2) = |-c|^(2)`
` Rightarrow |a^(2)| |b^(2)| +2|a||b|cos theta =|c|^(2)`
` Rightarrow 1+1+2 cos theta =3`
` Rightarrow cos theta = 1/2 `
` Rightarrow theta = pi/3`
Angle between a and b is ` pi/3`