question_answer

If M denotes the mid-point of the line joining \[A\,(4\hat{i}+5\hat{j}-10\hat{k})\]and\[B\,(-\hat{i}+2\hat{j}+\hat{k})\]then equation of the plane through M and perpendicular to AB is

A)  \[\vec{r}.(-\,5\hat{i}-3\hat{j}+11\hat{k})+\frac{135}{2}=0\]

B)  \[\vec{r}.(\frac{3}{2}\hat{i}+\frac{7}{2}\hat{j}-\frac{9}{2}\hat{k})+\frac{135}{2}=0\]

C)  \[\vec{r}.(4\hat{i}+5\hat{j}-10\hat{k})+4=0\]

D)  \[\vec{r}.(-\hat{i}+2\hat{j}+\hat{k})+4=0\]