Physics - Vectors Question with Solution | TestHub

The vector $\vec{A}$ lies in the third quadrant and makes an angle $\theta$ with the negative X-axis.

The component of the vector along the negative X-axis is $A\cos \theta$, so $A_x=-A\cos \theta$.

The component of the vector along the negative Y-axis is $A\sin \theta$, so $A_y=-A\sin \theta$.

Therefore, the vector in standard resolved form is $\vec{A}=-A\cos \theta \hat{i}-A\sin \theta \hat{j}$.

Answer: $-A\cos \theta \hat{i}-A\sin \theta \hat{j}$