A) \[\vec{r}.\left( \frac{3}{2}\hat{i}+\frac{7}{2}\hat{j}-\frac{9}{2}\hat{k} \right)=45\]
B) \[\vec{r}.\left( -\hat{i}+2\hat{j}-\hat{k} \right)=\frac{135}{2}\]
C) \[\vec{r}.(5\hat{i}+3\hat{j}-11\hat{k})+\frac{135}{2}=0\]
D) \[\vec{r}.(5\hat{i}+3\hat{j}-11\hat{k})=\frac{135}{2}\]
Correct Answer: D
Solution :
[d] Mid-point of PQ is \[=\left( \frac{3}{2},\frac{7}{2},\frac{-9}{2} \right)\] DR of the normal is \[=(4-(-1),5-2,-10-1)\] \[=5,3,-11\] \[\therefore \] Eqn. of plane is \[5\left( x-\frac{3}{2} \right)+3\left( y-\frac{7}{2} \right)-11\left( z+\frac{9}{2} \right)=0\] \[\Rightarrow 5x+3y-11z=\frac{135}{2}\] \[\Rightarrow \,\,r.\,(5\hat{j}+3\hat{j}-11\hat{k})=\frac{135}{2}\]
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