If `veca+vecb+vecc=vec0, |veca| = 3, |vecb| = 5, |vecc| = 7`, then angle between `veca` and `vecb` is

Options

A. `pi//6`
B. `2pi//3`
C. `5pi//3`
D. `pi//3`

Answer

B

Explanation

Given `vec(a)+vec(b)+vec(c)=vec(0)`
`therefore vec(c)=-(vec(a)+vec(b)`
`Rightarrow |vec(c)|^(2)=|vec(a)|^(2)+|vecb|^(2)+2vec(a).vec(b)`
`Rightarrow |vec(c)|^(2)=|vec(a)|^(2)+|vecb|^(2)+2|vec(a)||vec(b)|cos theta`
`Rightarrow 15=30 cos theta Rightarrow cos theta=(1)/(2)`
`Rightarrow theta=(pi)/(3)`