If p times q = p times r and p cdot q = p cdo | vedclass

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(B) Given: $p 	imes q = p 	imes r$ and $p \cdot q = p \cdot r$ From $p 	imes q = p 	imes r$,we have: $p 	imes q - p 	imes r = 0$ $p 	imes (q -

Vedclass · Accepted Answer

$q = r$

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(B) Given: $p 	imes q = p 	imes r$ and $p \cdot q = p \cdot r$ From $p 	imes q = p 	imes r$,we have: $p 	imes q - p 	imes r = 0$ $p 	imes (q - r) = 0$ This implies that $p$ is parallel to $(q - r)$ or $(q - r) = 0$. From $p \cdot q = p \cdot r$,we have: $p \cdot q - p \cdot r = 0$ $p \cdot (q - r) = 0$ This implies that $p$ is perpendicular to $(q - r)$ or $(q - r) = 0$. Since $p$ cannot be both parallel and perpendicular to the same non-zero vector $(q - r)$,it must be that $(q - r) = 0$. Therefore,$q = r$ (assuming $p 
eq 0$). Hence,option $B$ is correct.

If $p \times q = p \times r$ and $p \cdot q = p \cdot r$,then $\ldots . . .$.

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