One of the rectangular components of a force of $40 \ N$ is $20 \sqrt{3} \ N$. What is the other rectangular component (in $N$)?

The magnitude of vectors $\overrightarrow{ OA }, \overrightarrow{ OB }$ and $\overrightarrow{ OC }$ in the given figure are equal. The direction of $\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }$ with the $x$-axis will be

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.]

Given vector $\vec{A} = 2\hat{i} + 3\hat{j}$,the angle between $\vec{A}$ and the $y$-axis is:

$A$ person walks $25.0^{\circ}$ north of east for $3.18 \,km$. How far would she have to walk due north and then due east to arrive at the same location?

Find the angle the vector $\sqrt{3} \hat{i} - \hat{j}$ makes with the positive $x$-axis. (in $^{\circ}$)