If `a+b+c=0` and `|a|=5, |b|=3` and `|c|=7`, then angle between a and b is

Options

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

Answer

B

Explanation

Given, `|a|=5, |b|=3, |c|=7 and a+b+c=0`
`impliesa+b=-c`
On squaring both sides, we get
`(a+b)^(2)=(-c)^(2)implies|a+b|^(2)=|c|^(2)`
`implies|a|^(2)+|b|^(2)+2a*b=|c|^(2)`
`[because theta` be the angle between a and b]
`implies(5)^(2)+(3)^(2)+2|a||b|cos theta =(7)^(2)`
`implies25+9+2.5.3cos theta =49`
`implies30 cos theta =15`
`implies cos theta =1/2=cos 60^(@)`
`impliestheta =(pi)/(3)`