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Let veca and vecb be two unit vectors. I...

Let `veca` and `vecb` 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:

Text Solution

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`(vec(a)+2vec(b)).(5vec(a)-4vec(b))=0`
`=5a^(2)-4ab cos theta+10 ab cos theta - 8b^(2)=0`
`5-4 cos theta+10 cos theta-8=0 [a=b=1]`
`= -3+6 cos theta =0`
`cos theta = 1//2, theta = 60^(@)`
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