JEE Advanced Three Dimensional Geometry questions

5 Mathematics questions on Three Dimensional Geometry as asked in JEE Advanced, newest first.

A straight line drawn from the point P(1,3,2), parallel to the line (x-2)/1=(y-4)/2=(z-6)/1, intersects the plane L_1: x-y+3z=6 at the point Q. Another straight line which passes through Q and is perpendicular to the…
2024
Let R^3 denote the three-dimensional space. Take two points P=(1,2,3) and Q=(4,2,7). Let dist(X,Y) denote the distance between two points X and Y in R^3. Let S = \ X ∈ R^3 : (dist(X,P) )^2 - (dist(X,Q) )^2 = 50 \ and T…
2024
Let γ ∈ R be such that the lines L_1 : (x+11)/1 = (y+21)/2 = (z+29)/3 and L_2 : (x+16)/3 = (y+11)/2 = (z+4)/(γ) intersect. Let R_1 be the point of intersection of L_1 and L_2. Let O = (0,0,0), and n denote a unit normal…
2024
Let Q be the cube with the set of vertices \(x_1, x_2, x_3) ∈ R^3 : x_1, x_2, x_3 ∈ \0,1\ \. Let F be the set of all twelve lines containing the diagonals of the six faces of the cube Q. Let S be the set of all four…
2023
Let ell_1 and ell_2 be the lines r_1 = λ(i+j+k) and r_2 = (j-k)+μ(i+k), respectively. Let X be the set of all the planes H that contain the line ell_1. For a plane H, let d(H) denote the smallest possible distance…
2023

Practise Three Dimensional Geometry the way it is asked

A timed set of real JEE Advanced Three Dimensional Geometry questions, graded as the exam grades. No sign-up.