NOTE :
By perpendicular component of $\vec{F}$, I mean a vector which is a component of $\vec{F}$, but perpendicular to it.
In the image above, the red vectors are a possible set of rectangular components of $\vec{F}$, and blue vector is the sine component of cos component of $\vec{F}$, ie, perpendicular component of $\vec{F}$.
Now, logically, the perpendicular component of $\vec{F}$ should be zero, since its projection is zero.
But if we consider the image above, the Perpendicular component, $|\vec{F}|\cos\theta\sin\theta$, is not zero.
What is the cause of this discrepancy, and how to take components properly?