Let `hata and hatb` be two unit vectors. If the vectors `vecc=hata+2hatb and vecd=5hata-4hatb` are perpendicular to each other then the angle between `hata and hatb` is (A) `pi/2` (B) `pi/3` (C) `pi/4` (D) `pi/6`

Options

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

Answer

C

Explanation

Given, c and d are perpendicular to each other,
`therefore c*d = 0`
`rArr (hata + 2hatb)*(5 hata - 4 hatb) = 0 `
`rArr 5 hata * hata - 4 hat a *hat b + 10 hat b * hata - 8 hatb * hatb = 0 `
` rArr 6 hata * hatb = 3 `
`rArr hata *hatb = (1)/(2)`
So, the angle between `hata and hatb` is `(pi)/(3)`.