JEE Main 2024 — Three Dimensional Geometry Questions with Solutions

Let a line passing through the point ( - 1 , 2 , 3 ) intersect the lines L 1 : x - 1 3 = y - 2 2 = z + 1 - 2 at M ( α ,…

If d 1 is the shortest distance between the lines x + 1 = 2 y = - 12 z , x = y + 2 = 6 z - 6 and d 2 is the shortest di…

If the shortest distance between the lines x − λ − 2 = y − 2 1 = z − 1 1 and x − 3 1 = y − 1 − 2 = z − 2 1 is 1 , then…

Consider a line L passing through the points P(1,2,1) and Q(2,1,-1). If the mirror image of the point A(2,2,2) in the l…

Let the position vectors of the vertices A , B and C of a triangle be 2 i ^ + 2 j ^ + k ^ , i ^ + 2 j ^ + 2 k ^ and 2 i…

If the shortest distance between the lines (x+2)/(2)=(y+3)/(3)=(z-5)/(4) and (x-3)/(1)=(y-2)/(-3)=(z+4)/(2) is 383 √(5)…

The distance, of the point ( 7 , - 2 , 11 ) from the line x - 6 1 = y - 4 0 = z - 8 3 along the line x - 5 2 = y - 1 -…

If the shortest distance between the lines (x-λ)/(2)=(y-4)/(3)=(z-3)/(4) and (x-2)/(4)=(y-4)/(6)=(z-7)/(8) is 13√(29),…

If the shortest distance between the lines $\begin{array}{ll} L_1: \vec{r}=(2+\lambda) \hat{i}+(1-3 \lambda) \hat{j}+(3…

Let the image of the point ( 1 , 0 , 7 ) in the line x 1 = y - 1 2 = z - 2 3 be the point ( α , β , γ ) . Then which on…