If the lines (x-1)/(1)=(y-2)/(2)=(z+3)/(1) and (x-a)/(2)=(y+2)/(3)=(z-3)/(1) intersects at the point P , then the distance of the point P from the plane z=a is :

3D Geometry: If the lines (x-1)/(1)=(y-2)/(2)=(z+3)/(1) and… | JEE Main 2023

JEE Main 2023 (Online) 29th January Evening ShiftQuestion 1

If the lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z+3}{1}$ and $\frac{x-a}{2}=\frac{y+2}{3}=\frac{z-3}{1}$ intersects at the point $P$, then the distance of the point $P$ from the plane $z=a$ is :

3D Geometry

$16$$28$✓ Correct answer$10$$22$

Solution

Equate points: $2+2t=-2+3s$, $-3+t=3+s$ give $s=16,t=22$; then $1+t=a+2s$ gives $a=-9$. $P$ has $z=19$, distance from $z=-9$ is $28$.

3D Geometry - JEE Mathematics question (JEE Main 2023 (Online) 29th January Evening Shift)

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