What displacement must be added to the displacement $25\hat i - 6\hat j\,\,m$ to give a displacement of $7.0\, m$ pointing in the $X- $direction

The sum of two forces $\overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ is $\overrightarrow{\mathrm{R}}$ such that $|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .$ The angle $\theta$ (in degrees) that the resultant of $2 \overrightarrow{\mathrm{P}}$ and $\overrightarrow{\mathrm{Q}}$ will make with $\overrightarrow{\mathrm{Q}}$ is

Three concurrent forces of the same magnitude are in equilibrium. What is the angle between the forces  Also name the triangle formed by the forces as sides

Two equal forces ($P$ each) act at a point inclined to each other at an angle of $120^°$. The magnitude of their resultant is

The vector sum of two forces is perpendicular to their vector differences. In that case, the forces

$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. Find $\overrightarrow{A B}+\overrightarrow{B C}+\overrightarrow{C A}=.......$