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Question
If \[\vec{A} \times \vec{B} = 0\] can you say that
(a) \[\vec{A} = \vec{B} ,\]
(b) \[\vec{A} \neq \vec{B}\] ?
Solution
If \[\vec{A} \times \vec{B} = 0\], then both the vectors are either parallel or antiparallel, i.e., the angle between the vectors is either \[0^\circ \text { or } 180^\circ\].
\[\vec{A} \vec{ B } \sin\ \theta \ \hat { n } = 0.......\left(\because \sin0^\circ= \sin180^\circ = 0\right)\]
Both the conditions can be satisfied:
(a) \[\vec{A} = \vec{B} ,\] i.e., the two vectors are equal in magnitude and parallel to each other
(b) \[\vec{A} ≠ \vec{B} ,\] i.e., the two vectors are unequal in magnitude and parallel or anti parallel to each other.
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