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

Options

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

Answer

B

Explanation

Given , a + b + c = 0
and ` |a| = 5, |b| = 3, |c| = 7 `
` rArr a + b = - c `
On squaring both sides, we get
` (a + b ) ^ 2 = ( - c ) ^ 2 `
`rArr |a + b| ^ 2 = |c| ^ 2 `
` rArr |a| ^ 2 + |b| ^ 2 + 2a * b = |c| ^ 2 `
` ( because theta ` be the angle between a and b )
` rArr ( 5 ) ^ 2 + ( 3 ) ^ 2 + 2| a||b| cos theta = ( 7 ) ^ 2 `
` rArr 25 + 9 + 2* 5 * 3 * cos theta = 49`
` rArr 30 cos theta = 15 `
` rArr cos theta = ( 1 ) / ( 2 ) = cos 60 ^@ `
`rArr theta = ( pi) / ( 3 ) `