Answer: Option C
:
C

So component of A along direction of B is $Acos{120}^{\circ }=-Asin30=-5$
$[\because cos(90+\theta )=-sin\theta ]$
Here we can see if just measure the shadow you will get a $cos60=\frac{a}{2}=5$

But since this 5 is in the opposite direction of vector B so we say that the component of A along the
direction B is -5.
Now component in the perpendicular direction of B is
$Asin\left({120}^{\circ }\right)=Acos30=5\sqrt{3}$
$[\because sin(90+\theta )=cos\theta ]$

Just the shadow measurement is a cos ${30}^{\circ }$ and it's in the perpendicular direction, so no need to
change sign.
So component along the direction is always $acos\theta$ and in perpendicular direction is $asin\theta$. This will take care of sign so don't worry.