Find the unit vector of a vector whose coordinates are $(8, 6)$.

The component of a vector $\vec{A}$ along a direction making an angle $\theta$ with it is given by $A \cos \theta$. What can be said about the magnitude of this component?

For the components of a vector $\vec{A} = (3 \hat{i} + 4 \hat{j} - 5 \hat{k})$,match the following columns.

Column $I$	Column $II$
$(A)$ Component along $x$-axis	$(p)$ $5 \text{ unit}$
$(B)$ Component along vector $(2 \hat{i} + \hat{j} + 2 \hat{k})$	$(q)$ $4 \text{ unit}$
$(C)$ Component along $(6 \hat{i} + 8 \hat{j} - 10 \hat{k})$	$(r)$ $0$
$(D)$ Component along $(-3 \hat{i} - 4 \hat{j} + 5 \hat{k})$	$(s)$ None

If $\vec{A}$ and $\vec{B}$ are two non-zero vectors such that $|\vec{A} + \vec{B}| = \frac{|\vec{A} - \vec{B}|}{2}$ and $|\vec{A}| = 2|\vec{B}|$,then the angle between $\vec{A}$ and $\vec{B}$ is

$A$ particle is moving with speed $6 \, m/s$ along the direction of $\vec{A} = 2\hat{i} + 2\hat{j} - \hat{k}$. What is its velocity vector?

Let $\theta$ be the angle between vectors $\vec{A}$ and $\vec{B}$. Which of the following figures correctly represents the angle $\theta$?