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Vector Algebra

Question
CBSEENMA12034238
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If either straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top space space space or space space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top comma space then space space space space straight a with rightwards arrow on top cross times space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top. Is the  converse true? Justify your answer with an example.

Solution

If straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top space space or space space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top space then space straight a with rightwards arrow on top space cross times space straight b with rightwards arrow on top space equals 0 with rightwards arrow on top.
But the converse is not true, i.e., if straight a with rightwards arrow on top cross times straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top then straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top space space or space space straight b with rightwards arrow on top space equals space 0 with rightwards arrow on top may not hold.
        For example, consider the vectors straight a with rightwards arrow on top space equals space straight i with hat on top comma space space straight b with rightwards arrow on top space equals straight i with hat on top space.
                          Then straight a with rightwards arrow on top space not equal to space 0 with rightwards arrow on top also,    straight b with rightwards arrow on top space not equal to space 0 with rightwards arrow on top    but straight a with rightwards arrow on top cross times straight b with rightwards arrow on top space equals space straight i with hat on top space cross times space straight i with hat on top space equals space 0 with rightwards arrow on top.

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