$A$ man walks $20\,m$ at an angle $60^{\circ}$ north of east. How far towards the east has he travelled?

The $Y$-component of velocity is $20$ and the $X$-component of velocity is $10$. The direction of motion of the body with the horizontal at this instant is

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

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.

$A$ 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.