The square of the distance of the image of the point (6,1,5) in the line x-1/3=y/2=z-2/4 , from the origin is

Mathematics · 3D Geometry

JEE Main 2024 — 9 April, Shift 2 — Question 27

The square of the distance of the image of the point $(6,1,5)$ in the line $\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$ , from the origin is $\qquad$

Numerical answer — enter this value.

Let $\mathrm{M}(3 \lambda+1,2 \lambda, 4 \lambda+2)$

$\overrightarrow{\mathrm{AM}} \cdot \overrightarrow{\mathrm{b}}=0$

$\Rightarrow \quad 9 \lambda-15+4 \lambda-2+16 \lambda-12=0$

$\Rightarrow \quad 29 \lambda=29$ $\Rightarrow \lambda=1$

$\mathrm{M}(4,2,6), \mathrm{I}=(2,3,7)$

Required Distance $=\sqrt{4+9+49}=\sqrt{62}$

Answer key and solution verified before publishing.

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