JEE Main 2023 — Three Dimensional Geometry Questions with Solutions

Let ( α , β , γ ) be the image of point P ( 2 , 3 , 5 ) in the plane 2 x + y - 3 z = 6 . Then α + &…

A vector v → in the first octant is inclined to the x axis at 60 ° , to the y -axis at 45 ° and to the…

If the shortest distance between the line joining the points 1 , 2 , 3 and 2 , 3 , 4 , and the line x - 1 2 = y + 1 - 1…

Let the plane P : 8 x + α 1 y + α 2 z + 12 = 0 be parallel to the line L : x + 2 2 = y - 3 3 = z + 4 5 . If t…

The shortest distance between the lines x - 2 3 = y + 1 2 = z - 6 2 and x - 6 3 = 1 - y 2 = z + 8 0 is equal to ______

Let a unit vector O P → make angle α , β , γ with the positive directions of the co-ordinate axes…

The line, that is coplanar to the line x + 3 - 3 = y - 1 1 = z - 5 5 , is

Let the plane containing the line of intersection of the planes P 1 :   x + λ + 4 y + z = 1 and P 2 :  …

If λ 1 < λ 2 are two values of λ such that the angle between the planes P 1 : r → ( 3 i ^ - 5…

Let the image of the point P ( 1 ,   2 ,   6 )   in the plane passing through the points A ( 1 ,  …