JEE Main 2026 · 5 Apr · Shift 1 · Mathematics Q13

MathematicsSingle correct+4 / -1Question 13 of 75

The square of the distance of the point $P(5,6,7)$ from the line $\dfrac{x-2}2=\dfrac{y-5}3=\dfrac{z-2}4$ is equal to:

Answer and worked solution

Official answer: C

Setup. $A(2,5,2)$ is on the line, with direction $\vec d=(2,3,4)$ , $|\vec d|^2=29$ . $\vec{AP}=(3,1,5)$ , $|\vec{AP}|^2=35$ .

Projection. $\vec{AP}\cdot\vec d=6+3+20=29$ , so the squared projection is $29^2/29=29$ .

Distance squared: $35-29=6$ .

(C)

Topics:Angles and distances Equation of a line in space

JEE Main 2026 · 5 Apr · Shift 1, Mathematics question 13