The projection of a vector $\vec{r} = 3\hat{i} + \hat{j} + 2\hat{k}$ on the $xy$-plane has magnitude:

Find the angle in degrees between the vector $\vec{A} = \hat{i} + \hat{j} + \sqrt{2} \hat{k}$ and the $Z$-axis.

The resultant of these forces $\overrightarrow{OP}, \overrightarrow{OQ}, \overrightarrow{OR}, \overrightarrow{OS}$ and $\overrightarrow{OT}$ is approximately $\ldots \ldots \text{N}$.
[Take $\sqrt{3}=1.7, \sqrt{2}=1.4$. Given $\hat{i}$ and $\hat{j}$ are unit vectors along $x, y$ axes.]

Which one of the following pairs cannot be the rectangular components of a force vector of $10 \, N$?

Add vectors $\vec{A}$,$\vec{B}$,and $\vec{C}$,each having a magnitude of $50 \text{ units}$ and inclined to the $X$-axis at angles $45^{\circ}$,$135^{\circ}$,and $315^{\circ}$ respectively.

The velocity of a particle having a magnitude of $10 \ m/s$ in the direction of $60^{\circ}$ with the positive $X$-axis is: