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If overset(to)(a) " and " overset(to)(b...

If `overset(to)(a) " and " overset(to)(b)_(1)` are two unit vectors such that `overset(to)(a) +2overset(to)(b)` and `5overset(to)(a) -4overset(to)(b)` are perpendicular to each other then the angle between `overset(to)(a) " and " overset(to)(b)` is

A

`45^(@)`

B

`60^(@)`

C

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

D

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

Text Solution

Verified by Experts

The correct Answer is:
B
Since `(vec(a) +2vec(b)) .(5vec(a) -4vec(a))=0`
`rArr 5|vec(a)|^(2)+6vec(a).vec(b)-8|vec(b)|^(2)=0`
`rArr 6 vec(a)"." vec(b) =3 [ :' |vec(a)|=|vec(b)|=1]`
`rArr cos 0 = (1)/(2) rArr 0= 60^(@)`
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