Given $\vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k})$,$\vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k})$. The value of $(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

Two forces,each numerically equal to $10$ $dyne$,are acting as shown in the adjoining figure. The magnitude of the resultant force is ......... $dyne$.

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are at an angle of $60^{\circ}$ with each other. Their resultant makes an angle of $45^{\circ}$ with $\overrightarrow{a}$. If $|\overrightarrow{b}| = 2 \text{ units}$,then $|\overrightarrow{a}|$ is:

At what angle do two forces $(x + y)$ and $(x - y)$ act so that their resultant is $\sqrt{x^2 + y^2}$?

Explain the triangle method (head-to-tail method) of vector addition.

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