The vectors a(x)=(cosxi + sinxj) and b(x)=xi + sinxj {where i and j are unit vectors) are collinear for what values of x?

I think the ans is all values of x for which sinx=0 or cosx=x.If my ans is correct,I will definitely explain,pls tell whether it is correct or not.

the options given r -

a) unique value of x, 0<x<pi/6

b) unique value of pi/6<x<pi/3

c) no value of x

d) infinite values of x, 0<x<pi/3

I think the ans is option(b) since cosx=x has a unique soln in (pi/6,pi/3).Is it correct?

For two vecotrs a and b to be collinear

a = b

so,

(cosx)i + (sinx)j = (xi + (sinx)j) 

=> cosx = x and sinx = sinx

=> = 1

.: x = cosx

this eqn has only one solution which occurs very near to x=pi/4, so option B is correct