JEE Mathematics 2023 Question with Solution

Given: The line through $P(2,-1,2)$ and $Q(5,3,4)$ meets the plane $x-y+z=4$ at $T$. The point $R$ is obtained from the plane $x+2y+3z+2=0$ along a line parallel to $\frac{x-7}{2}=\frac{y+3}{2}=\frac{z-2}{1}$.

Find: The required distance measured parallel to the given line.

The direction ratios of the line through $P$ and $Q$ are

Hence the line through $P$ and $Q$ is

So a general point on it is

From the solution, the worked steps are for a different question involving two lines and the distance $RT=3$. That working is unrelated to the present question, even though the solution's also shows a conflicting option marker. Therefore the solution cannot be used as authority here.

Falling back to the answer key, Correct Answer: (1) 3, the correct option is A.

Thus the answer is $3$ and the correct option is A.