KVPY Sample Paper KVPY Stream-SX Model Paper-22

Distance of the point \[P\,(2,\,\,-3,\,\,4)\] from plane \[\bar{r}.(\hat{i}+\hat{j}+\hat{k})=5\] measured parallel to x-axis, is

A) 1

B) \[\sqrt{2}\]

C) 2

D) 4

Correct Answer: C

Solution :

Equation of a line parallel to x-axis and passes through \[P\,(2,\,\,-3,\,\,4)\]

\[\frac{x-2}{1}=\frac{y+3}{0}=\frac{z-4}{0}=\lambda \]

Point on it \[\,(\lambda +2,\,\,-3,\,\,4)\]

it will satisfy plane

Point on plane \[Q\,(+\,\,4,\,\,-3,\,\,4)\]

hence dis \[PQ=2\]