Match List-I with List-II
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List-I |
List-II |
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| A. |
Distance of the point (1, -1, 1) from the plane $\vec{r} . (\hat{i}-\hat{j}+\hat{k})=2$, is |
I. |
$x+y+z=2$ |
| B. |
$\vec{r} . (\hat{i}+\hat{j}+\hat{k})=2$ |
II. |
$-x+y+z=5$ |
| C. |
Distance of a point (1, -1, 1) from the plane $\vec{r} . (\hat{i}+\hat{j}-\hat{k})=5$, is |
III. |
$\frac{1}{\sqrt{3}}$ |
| D. |
$\vec{r} . (-\hat{i}+\hat{j}+\hat{k})=5$, |
IV. |
$2 \sqrt{3}$ |
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 4
A. $d=\left|\frac{1+1+1-2}{\sqrt{1^2+(-1)^2+1^2}}\right|=\frac{1}{\sqrt{3}}$ (III)
B. $\vec{r} . (\hat{i}+\hat{j}+\hat{k})=2 \Rightarrow x+y+z=2$ (I)
C. $d=\left|\frac{1-1-1-5}{\sqrt{1^2+1^2+(-1)^2}}\right|=\frac{6}{\sqrt{3}}=2 \sqrt{3}$ (IV)
D. $\vec{r} . (-\hat{i}+\hat{j}+\hat{k})=5 \Rightarrow -x+y+z=5$ (II)
Option: D