The component of a vector $A$ at an angle $\theta$ to itself is, \[A_x=A\cos\theta\] At right angle, \[A_x=A\cos90°=0\] Hence, the magnitude of component of a vector right angle to itself is zero.

Show that two vectors of different magnitudes cannot be combined to give zero resultant, whereas three vectors can be.

The magnitude of a vector has doubled, its direction remaining the same. Can you conclude that the magnitude of each component of the vector has doubled?