The angle made by the vector $\vec{A} = \hat{i} + \hat{j}$ with the $x$-axis is ....... $^\circ$.

For the given vector $\vec{A} = 3\hat{i} - 4\hat{j} + 10\hat{k}$,the ratio of the magnitude of its component on the $x-y$ plane to the component on the $z$-axis is:

If the magnitude of a vector $\overrightarrow{p}$ is $25 \text{ units}$ and its $y$-component is $7 \text{ units}$, then its $x$-component is (in $\text{ units}$)

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

$A$ displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in the $x-y$ plane are .........

The component of vector $\overrightarrow{A}=a_x \hat{i}+a_y \hat{j}+a_z \hat{k}$ along the direction of $\hat{i}-\hat{j}$ is