For any two vectors a and b,if a times b = 0, | vedclass

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(D) The cross product of two vectors $a$ and $b$ is defined as $a 	imes b = |a||b| \sin(	heta) \hat{n}$,where $	heta$ is the angle between the vect

Vedclass · Accepted Answer

None of these

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(D) The cross product of two vectors $a$ and $b$ is defined as $a 	imes b = |a||b| \sin(	heta) \hat{n}$,where $	heta$ is the angle between the vectors.If $a 	imes b = 0$,then $|a||b| \sin(	heta) = 0$.This implies that either $|a| = 0$,$|b| = 0$,or $\sin(	heta) = 0$.If $\sin(	heta) = 0$,then $	heta = 0$ or $	heta = \pi$,which means the vectors $a$ and $b$ are parallel or collinear.Since the condition $a 	imes b = 0$ can hold even if $a 
eq 0$ and $b 
eq 0$ (when they are parallel),none of the options $A, B,$ or $C$ are necessarily true.Therefore,the correct option is $D$.

For any two vectors $a$ and $b$,if $a \times b = 0$,then

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