question_answer

Can the magnitude of the rectangular component of a vector be greater than the magnitude of that vector?

Answer:

                No. For example, the rectangular components of vector \[\vec{A}\] are \[{{A}_{x}}=A\cos \theta \] and \[{{A}_{y}}=A\sin \theta \]. As both \[\sin \theta \] and \[\cos \theta \] can take values between \[-1\] and \[+1\], so the magnitudes of both \[{{A}_{x}}\] and \[{{A}_{y}}\] cannot be greater than A.