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The vector (veca+ 3vec b) is perpendicu...

The vector `(veca+ 3vec b)` is perpendicular to `(7vec a - 5vec b) and (vec a -4vec b)` is perpendicular to `(7vec a -2vec b)`. The angle between `vec a and vec b` is :

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

None of these

Text Solution

Verified by Experts

`(vec(a)+3vec(b)).(7vec(a)-5vec(b))=0`
`rArr 7a^(2)-15b^(2)+16 vec(a). vec(b)=0` …(i)
and, `(vec(a)-4vec(b)).(7vec(a)-2vec(b))=0`
`rArr 7a^(2)+8b^(2)-30 vec(a).vec(b)=0` …(ii)
By adding (i) and (ii)
`rArr -23b^(2)+46vec(a).vec(b)=0 rArr 2vec(a).vec(b)=b^(2)`
So `7a^(2)-15b^(2)+8b^(2)=0 rArr a^(2)=b^(2)`
`rArr 2ab cos theta=b^(2) rArr 2 cos theta=1`
`rArr theta=cos^(-1) (1//2)=60^(@)`
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