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 (A) `45^0` (B) `60^0` (C) `cos^-1(1/3)` (D) `cos^-1(2/7)`

Options

A. `45^(@)`
B. `60^(@)`
C. `cos^(-1)(1//3)`
D. `cos^(-1)(2//7)`

Answer

b

Explanation

Given that `veca and vecb` are two unit vectors.
` |veca|=1 and |vecb|=1`
Also given that `(veca + 2vecb) . (5veca - 4vecb) =0`
` or 5|veca|^(2) - 8 |vecb|^(2) - 4veca.vecb+ 10 vecb. Veca =0`
`or 5-8 + 6 veca. Vecb =0`
`or 6|veca||vecb| cos theta=3`
( where `theta` is the angle between `veca and vecb` )
`or cos theta = 1//2`
`or theta = 60^(@)`