Q. Which of the following are equations for the plane passing through the points $P(1,1,\ - 1),\ \mathcal{Q}(3,0,\ 2)$ and $R( - 2,\ 1,\ 0)$?
A) $\left( 2\widehat{i} - 3\widehat{j} + 3\widehat{k} \right) \bullet \left( (x + 2)\widehat{i} + (y - 1)\widehat{j} + \mathcal{z}\widehat{k} \right) = 0$
B) $x = 3 - t,\ y = - 11t,\ \mathcal{z} = 2 - 3t$
C) $(x + 2) + 11(y - 1) = 3\mathcal{z}$
D) $\left( 2\widehat{i} - \widehat{j} + 3\widehat{k} \right) \times \left( - 3\widehat{i} + \widehat{k} \right) \bullet \left( (x + 2)\widehat{i} + (y - 1)\widehat{j} + \mathcal{z}\widehat{k} \right) = 0$
Explanation
(d)
${\overrightarrow{V}}_{1},\ {\overrightarrow{V}}_{2},\ \overrightarrow{PS}$ are in the same plane
$\therefore\left( 2\widehat{i} - \widehat{j} + 3\widehat{k} \right) \times \left( - 3\widehat{i} + \widehat{k} \right) \bullet \left( (x + 2)\widehat{i} + (y - 1)\widehat{j} + \mathcal{z}\widehat{k} \right) = 0$
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Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.