A) (0, -3, 1)
B) (0, 7, 10)
C) (0, 7, -10)
D) (0, 3, 1)
Correct Answer: B
Solution :
\[A(3,2,0)\And B(1,2,3)\]all in the plane \[\Rightarrow \]\[\overline{AB}=2\hat{i}+0\hat{j}+(-3)\hat{k}\]is in the plane \[\therefore \]Vector normal of plane \[=\left( 2\hat{i}-3\hat{k} \right)\times \left( \hat{i}+5\hat{j}+4\hat{k} \right)\] \[=15\hat{i}-11\hat{j}+10\hat{k}\] \[\therefore \]equation of plane is \[\left( \overline{r}-\left( 3\hat{i}+2\hat{j}+0k \right) \right)\cdot \left( 15\hat{i}-11\hat{j}+10\hat{k} \right)=0\] \[\Rightarrow \]\[15x-11y+10z-23=0\]
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