JEE Main 2025 — Three Dimensional Geometry Questions with Solutions

Let a line pass through two distinct points P(-2,-1,3) and Q, and be parallel to the vector 3 i+2 j+2 k. If the distanc…

If the square of the shortest distance between the lines (x-2)/(1)=(y-1)/(2)=(z+3)/(-3) and (x+1)/(2)=(y+3)/(4)=(z+5)/(…

Let a=i+2 j+k and b=2 i+7 j+3 k . Let L₁: r=(-i+2 j+k)+λ a, λ R and L₂: r=(j+k)+µ b, µ R be two lines. If the line L₃ p…

Let the line passing through the points (-1,2,1) and parallel to the line (x-1)/(2)=(y+1)/(3)=(z)/(4) intersect the lin…

Let the values of λ for which the shortest distance between the lines (x-1)/(2)=(y-2)/(3)=(z-3)/(4) and (x-λ)/(3)=(y-4)…

Let P be the foot of the perpendicular from the point (1,2,2) on the line L: (x-1)/(1)=(y+1)/(-1)=(z-2)/(2). Let the li…

Let the vertices Q and R of the triangle P Q R lie on the line (x+3)/(5)=(y-1)/(2)=(z+4)/(3), Q R=5 and the coordinates…

Let L₁: (x-1)/(1)=(y-2)/(-1)=(z-1)/(2) and L₂: (x+1)/(-1)=(y-2)/(2)=(z)/(1) be two lines. Let L₃ be a line passing thro…

Let a line passing through the point (4,1,0) intersect the line L₁ ; (x-1)/(2)=(y-2)/(3)=(z-3)/(4) at the point A (α, β…

The line L₁ is parallel to the vector a=-3 i+2 j+4 k and passes through the point (7,6,2) and the line L₂ is parallel t…