Let the line L intersect the lines x-2=-y=z-1 , 2(x+1)=2(y-1)=z+1 and be parallel to the line (x-2)/(3)=(y-1)/(1)=(z-2)/(2) . Then which of the following points lies on L ?

3D Geometry: Let the line L intersect the lines x-2=-y=z-1 , 2(x+1)=2(y-1)=z+1… | JEE Main 2024

JEE Main 2024 (Online) 9th April Morning ShiftQuestion 1

Let the line $L$ intersect the lines $x-2=-y=z-1$, $2(x+1)=2(y-1)=z+1$ and be parallel to the line $\frac{x-2}{3}=\frac{y-1}{1}=\frac{z-2}{2}$. Then which of the following points lies on $L$?

3D Geometry

$\left(-\frac{1}{3},1,-1\right)$✓ Correct answer$\left(-\frac{1}{3},-1,1\right)$$\left(-\frac{1}{3},1,1\right)$$\left(-\frac{1}{3},-1,-1\right)$

Solution

Points $(2+a,-a,1+a)$ and $(-1+b,1+b,-1+2b)$ with difference parallel to $(3,1,2)$: $4a+2b=-6$ and $3a=-4$, so $a=-\frac43$, $b=-\frac13$. Then $L$ passes through $(\frac23,\frac43,-\frac13)$ with direction $(3,1,2)$; at $x=-\frac13$ it gives $(-\frac13,1,-1)$.

3D Geometry - JEE Mathematics question (JEE Main 2024 (Online) 9th April Morning Shift)

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