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

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

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

The angles which the vector $\vec{A} = 3\hat{i} + 6\hat{j} + 2\hat{k}$ makes with the coordinate axes are

$A$ plane covers $500 \,m$ in a direction $60^o$ with the runway while starting the flight. Find the distance covered by the plane in the horizontal and vertical directions.

$A$ certain vector in the $xy$-plane has an $x$-component of $4 \,m$ and a $y$-component of $10 \,m$. It is then rotated in the $xy$-plane so that its $x$-component is doubled. Then its new $y$-component is (approximately) (in $\,m$)