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# If either $\stackrel{\to }{a}=\stackrel{\to }{0}\mathrm{or}\stackrel{\to }{b}=\stackrel{\to }{0},\mathrm{then}\stackrel{\to }{a}×\stackrel{\to }{b}=\stackrel{\to }{0}.$ Is the converse true? Justify your answer with an example.

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## $\mathrm{If}\stackrel{\to }{a}=\stackrel{\to }{0}\text{or}\stackrel{\to }{b}\text{=0, then}\left|\stackrel{\to }{a}\right|\left|\stackrel{\to }{b}\right|\mathrm{sin}\theta \stackrel{^}{n}=\stackrel{\to }{0.}\phantom{\rule{0ex}{0ex}}⇒\stackrel{\to }{a}×\stackrel{\to }{b}=\stackrel{\to }{0}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\text{But the converse is not true as whenever}\stackrel{\to }{a}\text{×}\stackrel{\to }{b}\text{=}\stackrel{\to }{0}\text{, we cannot be sure that either}\stackrel{\to }{a}\text{=}\stackrel{\to }{0}\text{or}\stackrel{\to }{b}\text{=}\stackrel{\to }{0}\text{.}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\text{For example:}\phantom{\rule{0ex}{0ex}}\stackrel{\to }{a}=\stackrel{^}{i}+2\stackrel{^}{j}+3\stackrel{^}{k}\phantom{\rule{0ex}{0ex}}\stackrel{\to }{b}=\stackrel{^}{i}+2\stackrel{^}{j}+3\stackrel{^}{k}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\text{Here,}\phantom{\rule{0ex}{0ex}}\stackrel{\to }{a}\text{≠0}\phantom{\rule{0ex}{0ex}}\stackrel{\to }{b}\text{≠0}\phantom{\rule{0ex}{0ex}}\text{But}\stackrel{\to }{a}×\stackrel{\to }{b}=\left|\begin{array}{ccc}\stackrel{^}{i}& \stackrel{^}{j}& \stackrel{^}{k}\\ 1& 2& 3\\ 1& 2& 3\end{array}\right|\phantom{\rule{0ex}{0ex}}=0\stackrel{^}{i}+0\stackrel{^}{j}+0\stackrel{^}{k}\phantom{\rule{0ex}{0ex}}=\stackrel{\to }{0}$  Suggest Corrections  0      Similar questions  Related Videos   Introduction
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