• # question_answer The plane which bisects the line segment joining the points $(-3,-3,4)$ and $(3,7,6)$ at right angles, passes through which one of the following points? A)  $(-2,3,5)$ B) $(4,-1,7)$ C)  $(2,1,3)$ D) $(4,1,-2)$

 $A(-3,3,4),(3,7,6)$ $Mid\text{ }point\Rightarrow (0,2,5)$ $\overrightarrow{n}=\overrightarrow{AB}=6\hat{i}+10\hat{j}+2\hat{k}$ 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.