1.

Let hata and hatb be two unit vectors. If the vectors c=hata+2hatb and d=hata-4hatb are perpendicular to each other, then the angle between hata and hatb is

Answer»

`(pi)/(6)`
`(pi)/(2)`
`(pi)/(3)`
`(pi)/(4)`

Solution :Given, c and d are PERPENDICULAR to each other,
`thereforec*d = 0`
`RARR (hata + 2hatb)*(5 hata - 4 HATB) = 0 `
`rArr 5 hata * hata - 4 HAT a *hat b + 10 hat b * hata - 8 hatb * hatb = 0 `
` rArr6 hata * hatb= 3 `
`rArr hata *hatb= (1)/(2)`
So, the angle between `hata and hatb` is `(pi)/(3)`.


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