Let `vec a`be a unit vector and `vec b`a non-zero vector not parallel to `vec a` The angles of the triangle, two of whose sides are represented by `sqrt3 (vec a xx vec b) and (vec b -(vec a .vecb) veca` are

Options

A. `30^(@), 90^(@), 60^(@)`
B. `45^(@), 45^(@), 90^(@)`
C. `60^(@), 60^(@), 60^(@)`
D. None of these

Answer

A

Explanation

`bar(AB) = sqrt(3)(baraxxbarb)`

`bar(AC) = vecb-(veca.vecb)veca` , `:'|veca|=|vecb|=1`
`rArr bar(AB)_|_bar(AC)`
`rArr angleBAC = 90^(@)`
Now, `|vec(AB)|^(2) = 3|vecaxxvecb|^(2)`
`|vec(AC)|^(2) = |veca|^(2)|vecb xx vecb|^(2)`
`rArr Ab = sqrt(3) AC`
`rArr tan C = (AB)/(AC) = sqrt(3)`
`rArr angleC = 60^(@) rArr angleA = 30^(@)`