A) \[(-2,3,5)\]
B) \[(4,-1,7)\]
C) \[(2,1,3)\]
D) \[(4,1,-2)\]
Correct Answer: D
Solution :
| \[A(-3,3,4),(3,7,6)\] |
| \[Mid\text{ }point\Rightarrow (0,2,5)\] |
| \[\overrightarrow{n}=\overrightarrow{AB}=6\hat{i}+10\hat{j}+2\hat{k}\] |
| Equation of plane \[\overrightarrow{r}.\overrightarrow{n}=\overrightarrow{a}.\overrightarrow{n}\] |
| \[\overrightarrow{r}.(6i+10\hat{j}+2\hat{k})=(0i+2\hat{j}+5\hat{k}).(6\hat{i}+10\hat{j}+2\hat{k})\] |
| \[3x+5y+z=15\] |
| \[(4,1,-2)\]satisfies it |
| \[\therefore \]Answer is D. |
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