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

$A$ 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.

Which one of the following pairs cannot be the rectangular components of a force vector of $10 \, N$?

$A$ force of $5 \, N$ acts at an angle of $60^\circ$ with the vertical. Find the vertical component of the force in $N$.

The $y$-component of vector $\vec{A}$ is $+3.0 \ m$. If $\vec{A}$ makes an angle of $30^{\circ}$ counterclockwise from the positive $y$-axis,the magnitude of $\vec{A}$ is (assume $\vec{A}$ is in the $x-y$ plane).

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