A) \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=0\]
B) \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=32\]
C) \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})=12\]
D) None of the above
Correct Answer: B
Solution :
The equation of plane parallel to- the plane \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})-7=0\]is \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})+\lambda =0\] ?(i) But the plane Eq. (i) passes through\[2\hat{i}-\hat{j}-4\hat{k}.\] \[\therefore \] \[(2\hat{i}-\hat{j}-4\hat{k}).(4\hat{i}-12\hat{j}-3\hat{k})+\lambda =0\] \[\Rightarrow \]\[8+12+12+\lambda =0\] \[\Rightarrow \]\[\lambda =-32\] So, the required plane is \[\vec{r}.(4\hat{i}-12\hat{j}-3\hat{k})-32=0\]
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