Question

If $\overrightarrow{A}\times \overrightarrow{B}=0$, can you say that (a) $\overrightarrow{A}=\overrightarrow{B},$ (b) $\overrightarrow{A}\ne \overrightarrow{B}$?

Answer 1

If $\overrightarrow{A}\times \overrightarrow{B}=0$, then both the vectors are either parallel or antiparallel, i.e., the angle between the vectors is either $0°\mathrm{or}180°$.
($\overrightarrow{A}\overrightarrow{B}\sin \theta \hat{n}=0$ $\because$ $\sin 0°=\sin 180°=0$)

Both the conditions can be satisfied:
(a) $\overrightarrow{A}=\overrightarrow{B},$ i.e., the two vectors are equal in magnitude and parallel to each other
(b) $\overrightarrow{A}\ne \overrightarrow{B}$, i.e., the two vectors are unequal in magnitude and parallel or anti parallel to each other