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If veca and vecb are two unit vectors su...

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)`

A

`45^(@)`

B

`60^(@)`

C

`cos^(-1)(1//3)`

D

`cos^(-1)(2//7)`

Text Solution

Verified by Experts

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^(@)`
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