What is the maximum number of components a vector can have when resolved in a plane?

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

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:

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

Two forces of magnitude $P$ and $Q$ acting at a point have a resultant $R$. The resolved part of $R$ in the direction of $P$ is of magnitude $Q$. The angle between the forces is:

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