1.

If vector `(hata+ 2hatb)` is perpendicular to vector `(5hata-4hatb)`, then find the angle between `hata and hatb`.

Answer» Correct Answer - `60^(@)`
`because (hata+ 2hatb) `is perpendicular to`(5hata-4hatb)`
`therefore (hata+ 2hatb) *( 5hata - 4hatb) =0`
`rArr 5hata*hata- 4hata*hatb+ 10 hatb*hata- 8hatb*hatb=0`
`rArr 5+ 6hata*hatb-8=0`
`rArr 6hata* hatb=3`
`rArr hata*hatb= (1)/(2)`
`rArr cos theta = (1)/(2)`
`rArr theta = 60^(@)`


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