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JEE Math Practice Question

The distance of the point $$(-1,2,3)$$ from the plane $$\vec{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=10$$ parallel to the line of the shortest distance between the lines $$\vec{r}=(\hat{i}-\hat{j})+\lambda(2 \hat{i}+\hat{k})$$ and $$\vec{r}=(2 \hat{i}-\hat{j})+\mu(\hat{i}-\hat{j}+\hat{k})$$ is :

  1. A.$$3 \sqrt{6}$$
  2. B.$$3 \sqrt{5}$$
  3. C.$$2 \sqrt{6}$$
  4. D.$$2 \sqrt{5}$$

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