# Why, here, the torque with respect to bob is zero?

here, as you see, is a diagram of a pendulum with moving pivot along x-y surface.

This picture was obtained from a journal in which this equation was written:

$$F_x l \cos\theta = F_y l \sin\theta$$

The explanations stated that this was because the torque of pivot with respect to the bob is zero, this is my approach:

$$\vec l= -l\sin\theta \hat i -l\cos\theta \hat j$$ $$\vec F= F_x \hat i + F_y \hat j$$ $$\vec \tau=\vec l \times \vec F = -F_y l\sin\theta \hat k + F_x l\cos\theta \hat k$$

so assuming $\vec\tau =0$ :

$$F_y l \sin\theta \hat k=F_x l\cos\theta \hat k$$

$$F_y l \sin\theta = F_x l \cos \theta$$

My question is Why can we say $\vec\tau = 0$ ?

$F_x$ and $F_y$ are components of a force. If the line of action of that force goes through the bob then the torque that the forces exerts about the bob is zero.