JEE Mathematics 2026 Question with Solution

Given: The image of point $P(1,2,a)$ in the line $\frac{x - 6}{3} = \frac{y - 7}{2} = \frac{7 - z}{2}$ is $Q(5,b,c)$.

Find: The value of $a^2 + b^2 + c^2$.

For reflection of a point in a line, the line is the perpendicular bisector of the segment joining the point and its image.

Take point $A(6,7,7)$ on the line and direction vector $\vec{p}=(3,2,-2)$. Any point $N$ on the line can be written as

so

Since $N$ is the midpoint of $PQ$,

Comparing the $x$-coordinates,

Hence,

Now compare the remaining coordinates:

Also, $PN$ is perpendicular to the line direction vector, so

Now,

Therefore,

Using $a+c=18$,

Now,

Therefore, the required value is $298$. The correct option is B.

The solution marks option D, but the worked solution gives $298$, which matches option B.