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

(N/A) No. Let a vector $\vec{A}$ have rectangular components $A_x$ and $A_y$ in a two-dimensional plane.
These components are given by:
$A_x = A \cos \theta$
$A_y = A \sin \theta$
where $A$ is the magnitude of the vector and $\theta$ is the angle it makes with the $x$-axis.
Since the maximum value of both $\sin \theta$ and $\cos \theta$ is $1$,the maximum value of the components $A_x$ and $A_y$ can only be equal to $A$ (when $\theta = 0^\circ$ or $90^\circ$).
Mathematically,since $|\cos \theta| \le 1$ and $|\sin \theta| \le 1$,it follows that $|A_x| \le |A|$ and $|A_y| \le |A|$.
Therefore,the magnitude of a rectangular component can never exceed the magnitude of the original vector.