If $\overrightarrow A = 4\hat i - 3\hat j$ and $\overrightarrow B = 6\hat i + 8\hat j$,then the magnitude and direction of $\overrightarrow A + \overrightarrow B$ will be:

If the resultant vector of vectors $\vec{A} = 4\hat{i} + 3\hat{j} + 6\hat{k}$ and $\vec{B} = -\hat{i} + 3\hat{j} - 8\hat{k}$ is parallel to a unit vector,then $\vec{R}$ is:

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ have equal magnitudes. If the magnitude of $\overrightarrow{A} + \overrightarrow{B}$ is equal to two times the magnitude of $\overrightarrow{A} - \overrightarrow{B}$, then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

$A$ vector of length $\ell$ is turned by an angle $\theta$. Find the change in the position vector of the tip.

The magnitudes of vectors $\overrightarrow{A}$,$\overrightarrow{B}$,and $\overrightarrow{C}$ are $12$,$5$,and $13$ units respectively,and $\overrightarrow{A} + \overrightarrow{B} = \overrightarrow{C}$. Then the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

Two forces whose magnitudes are in the ratio $5:3$ are acting at a point at an angle $60^{\circ}$ simultaneously. If the resultant of the two forces is $35 \ N$,then the magnitudes of the two forces respectively are