To compute torque, we need the position vector from the reference point to the point of application $P$.

1. Torque formula

For a force $\vec F = 4\hat i - 3\hat j$ applied at point $P$,

the torque about a point is

where $\vec r$ is the position vector from the reference point to $P$.

In 2D,

if $\vec r = x\hat i + y\hat j$ and $\vec F = F_x\hat i + F_y\hat j$.

Here,

so

Thus, to find the torques about $O$ and $Q$, we must know the coordinates of $P$ relative to $O$ and relative to $Q$.

2. Missing geometric figure

The problem states “A triangular plate is shown”, but the actual diagram is not provided here. Without the figure, the required position vectors $\overrightarrow{OP}$ and $\overrightarrow{QP}$ cannot be determined uniquely.

So the torques cannot be derived rigorously from the text alone.

3. Consistency check using options

Let the torque about $O$ be $\tau_O$ and about $Q$ be $\tau_Q$.

The options are:

• A: $-15+20\sqrt3,\; 15+20\sqrt3$
• B: $15-20\sqrt3,\; 15+20\sqrt3$
• C: $15+20\sqrt3,\; 15-20\sqrt3$
• D: $-15-20\sqrt3,\; 15-20\sqrt3$

Since the stored correct answer is D, the claimed torques are

These values are plausible for some triangle geometry, but without the diagram they cannot be independently verified.

4. Final conclusion

Because the essential figure is missing, a strict derivation is not possible from the provided information alone.

However, comparing with the stored answer, the marked option is:

which corresponds to