If the angle between the vectors `vec(a)=hat(i)+(cos x)hat(j)+hat(k)` and
`vec(b) =(sin^(2)x-sin x)hat(i)-(cos x)hat(j)+(3-4sin x)hat(k)`
is obutse and x in `(0,(pi)/(2))`, then the exhaustive set of values of 'x' is equal to-

Options

A. `x in (0,(pi)/(6))`
B. `x in ((pi)/(6),(pi)/(2))`
C. `x in ((pi)/(6),(pi)/(3))`
D. `x in ((pi)/(3),(pi)/(2))`

Answer

B

Explanation

` because vec(a).vec(b)lt0`
`implies (sin^(2)x-sinx)-cos^(2)x+3-4sinxlt0`
`implies2 sin ^(2)x-5sinx+2lt0`
`impliesubrace((sin x-2))_((-)ve) (2sinx-1)lt 0 impliessinxgt(1)/(2)`
`implies x epsilon ((pi)/(6),(pi)/(2))`