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JEE Main 2026 · 5 Apr · Shift 2, Mathematics question 15

If the distance of the point (a,2,5)(a,2,5) from the image of the point (1,2,7)(1,2,7) in the line x1=y−11=z−22\dfrac x1=\dfrac{y-1}1=\dfrac{z-2}2 is 4, then the sum of all possible values of a is equal to :

Choose one option
Answer and worked solution

Official answer: C

Foot. The line passes through (0,1,2)(0,1,2) with direction (1,1,2)(1,1,2). For the point (1,2,7)(1,2,7): (1,1,5)⋅(1,1,2)6=2\dfrac{(1,1,5)\cdot(1,1,2)}{6}=2, so the foot is (2,3,6)(2,3,6).

Image. 2(2,3,6)−(1,2,7)=(3,4,5)2(2,3,6)-(1,2,7)=(3,4,5).

Distance. (a−3)2+(2−4)2+(5−5)2=16(a-3)^2+(2-4)^2+(5-5)^2=16, so a=3±23a=3\pm2\sqrt3.

Sum: 6.

(C)

Topics:Equation of a line in spaceAngles and distances
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