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  • If either then . Is the converse true? Justify your answer with an example.

Q8  If either \vec a = \vec 0 \: \: or \: \: \vec b = \vec 0  then \vec a \times \vec b = \vec 0  . Is the converse true? Justify your answer with an example.

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best_answer

No, the converse of the statement is not true, as there can be two non zero vectors, the cross product of whose are zero. they are colinear vectors.

Consider an example

\vec a=\hat i +\hat j + \hat k

\vec b =2\hat i +2\hat j + 2\hat k

Here |\vec a| =\sqrt{1^2+1^2+1^2}=\sqrt{3}

|\vec b| =\sqrt{2^2+2^2+2^2}=2\sqrt{3}

\vec a \times \vec b=\begin{vmatrix} \hat i &\hat j &\hat k \\ 1&1 &1 \\ 2&2 &2 \end{vmatrix}=\hat i(2-2)-\hat j(2-2)+\hat k(2-2)=0

Hence converse of the given statement is not true. 

Posted by

Pankaj Sanodiya

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