If `veca` and `vecb` are two unit vectors such that `veca+2vecb` and `5veca-4vecb` are perpendicular to each other, then the angle between `veca` and `vecb` is

Options

A. `(pi)/(4)`
B. `(pi)/(3)`
C. `cos ^(-1)((1)/(3))`
D. `cos ^(-1)((2)/(7))`

Answer

B

Explanation

`" "(veca + 2vecb).(5veca- 4 vecb)=0 `
`5veca . veca- 8 vecb. vecb + 10 vecb. veca-4veca. vecb=0`
`" "5-8 + 10 cos theta - 4 cos theta = 0`
`" " 6 cos theta = 3`
`" "theta = (pi)/(3)`