HARD
JEE Main/Advance
IMPORTANT
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Find the shortest distance between any two opposite edges of a tetrahedron formed by the planes y+z=0,x+z=0,x+y=0,x+y+z=3a

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Important Questions on Three Dimensional Geometry

HARD
JEE Main/Advance
IMPORTANT
Equation of plane which passes through the point of intersection of lines x-13=y-21=z-32 and x-31=y-12=z-23 and at greatest distance from the point 0,0,0 is 
HARD
JEE Main/Advance
IMPORTANT
The non zero value of a for which the line 2x-y+3z+4=0=ax+y-z+2 and x-3y+z=0=x+2y+z+1 are co-planar is 
MEDIUM
JEE Main/Advance
IMPORTANT
A line L1 having direction ratios 1, 0, 1 lies on xz-plane is rotated about z-axis by an angle 90°. Now the new position of L1 is L2. The angle between L1 & L2 is
HARD
JEE Main/Advance
IMPORTANT
Given three point on x-y plane as O0, 0, A1, 0 & B-1,0. Point P is moving on the plane satisfying the condition PA·PB+3OA·OB=0. If the maximum & minimum values of PAPB are M & m respectively then the value of M2+m2 is
HARD
JEE Main/Advance
IMPORTANT
If r represents the position vector of point R in which the line AB cuts the plane CDE, where the position vectors of points A,B,C,D,E are respectively a=i^+2j^+k^,b=2i^+j^+2k^,c=-4j+4k^,d=2i^-2j^+2k^ and e=4i^+j^+2k^, then r2 is
HARD
JEE Main/Advance
IMPORTANT
Line L1 is parallel to vector α=-3i^+2j^+4k^ and passes through a point A7,6,2 and line L2 is parallel to a vector β=2i^+j^+3k^ and passes through a point B5,3,4. Now, a line L3 parallel to a vector r=2i^-2ȷ^-k^ intersects the lines L1 and L2 at points C and D respectively, then 4CD is equal to ?
HARD
JEE Main/Advance
IMPORTANT
The value of sec3θ, where θ is the acute angle between the plane faces of a regular tetrahedron, is
HARD
JEE Main/Advance
IMPORTANT
R and r are the circum-radius and in-radius of a regular tetrahedron respectively in terms of the length k of each edge. If R2+r2=pqk2, where p, qI, then absolute minimum value of p+q is