$A$ vector is represented by $3\,\hat i + \hat j + 2\,\hat k$. Its length in the $XY$ plane is

$A$ force of $5\, N$ acts on a particle along a direction making an angle of $60^\circ$ with the vertical. Its vertical component is.......$N$.

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

Can the magnitude of the rectangular components of a vector be greater than the magnitude of the vector itself? Explain.

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

$A$ vector in the $x-y$ plane makes an angle of $30^{\circ}$ with the $y$-axis. The magnitude of the $y$-component of the vector is $2 \sqrt{3}$. The magnitude of the $x$-component of the vector will be: