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vec(a) and vec(b) are unit vectors and a...

`vec(a)` and `vec(b)` are unit vectors and angle between them is `pi/k`. If `vec(a)+2vec(b)` and `5vec(a)-4vec(b)` are perpendicular to each other then find the integer value of k.

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The correct Answer is:
3
`(veca+2vecb).(5veca-4vecb)=0rArr 5a^(2)+10veca.vecb-8vecb^(2)-4veca.vecbrArr -3+6veca.vecb=0`
`rArr ab cos theta=3/6 rArr cos theta=1/2=theta=pi/3rArr k=3`
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