Answer: Option C
:
C
Well normally I guess by now you know how to find component of a vector along a given vector i.e.
(Magnitude of vector)×(cosine of angle between the two vectors)
This takes care of everything
$\Rightarrow$ In this case
$6\times cos{150}^{\circ }=6\times cos(90+60)$
= -$6sin{60}^{\circ }=-6\times \frac{\sqrt{3}}{2}=-3\sqrt{3}$
Caution:- Component of a vector is scalar. I agree it's tough to understand and remember trigonometric
identitiesintuitively. Also component of a vector is just the measure of the shadow
$\Rightarrow$

Here the length of shadow is $6cos{30}^{\circ }=6\times \frac{3}{2}=3\sqrt{3}$ but this component is on -ve x-axis.
But since the question asks the component along the direction of +vex-axis, so the component should be $-3\sqrt{3}$