3D Geometry: The equation of a line passing through the point (2,-1,1) and the… | JEE Main 2021

JEE Main 2021 (Online) 4th August Evening ShiftQuestion 1

The equation of a line passing through the point $(2,-1,1)$ and the point of intersection of the lines $2x-y-4=0=y+2z$ and $x+3z=0=2x+5z-1$, is

3D Geometry

$\dfrac{x-2}{1}=\dfrac{y+1}{-3}=\dfrac{z-1}{2}$$\dfrac{x-2}{1}=\dfrac{y+1}{3}=\dfrac{z-1}{-2}$✓ Correct answer$\dfrac{x-2}{1}=\dfrac{y+1}{3}=\dfrac{z-1}{2}$$\dfrac{x-2}{-1}=\dfrac{y+1}{3}=\dfrac{z-1}{2}$

Solution

$x+3z=0=2x+5z-1$ gives $z=-1,x=3$; then $y=2$ from $2x-y-4=0$ (and $y+2z=0$ holds). Intersection point $(3,2,-1)$; direction from $(2,-1,1)$ is $(1,3,-2)$.

3D Geometry - JEE Mathematics question (JEE Main 2021 (Online) 4th August Evening Shift)

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