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Vector Algebra

Question
CBSEENMA12034059
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If either vector straight a with rightwards arrow on top space equals space 0 with rightwards arrow on top space space or space straight b with rightwards arrow on top space equals space 0 comma space then space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0. But the converse need not be true. Justify your answer with an example. 

Solution

Let straight a with rightwards arrow on top space equals space straight i with hat on top space minus space 2 space straight j with hat on top space plus space 3 space straight k with hat on top comma space space straight b with rightwards arrow on top space equals space 12 space straight i with hat on top space plus space 3 space straight j with hat on top space minus space space 2 space straight k with hat on top be the two non-zero vectors
therefore space space space space space space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space left parenthesis 1 right parenthesis thin space left parenthesis 12 right parenthesis space plus space left parenthesis negative 2 right parenthesis thin space left parenthesis 3 right parenthesis space plus space left parenthesis 3 right parenthesis thin space left parenthesis negative 2 right parenthesis space equals space 12 minus 6 minus 6 space equals space 0 therefore space space space space space space space if space straight a with rightwards arrow on top space not equal to space 0 with rightwards arrow on top comma space space space straight b with rightwards arrow on top space not equal to space 0 with rightwards arrow on top comma space space even space that space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 0

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