MEDIUM
JEE Advanced
IMPORTANT
Earn 100

The four lines drawing from the vertices of any tetrahedron to the centroid of the opposite faces meet in a point whose distance from each vertex is k times the distance from each vertex to the opposite face, where k is

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Important Questions on Three Dimensional Coordinate System

MEDIUM
JEE Advanced
IMPORTANT
The shortest distance from 1,1,1 to the line of intersection of the pair of planes xy+yz+zx+y2=0 is
MEDIUM
JEE Advanced
IMPORTANT
The shortest distance between the two lines L1: x=k1; y=k2 & L2: x=k3; y=k4 is equal to
MEDIUM
JEE Advanced
IMPORTANT
A=l1m1n1l2m2n2l3m3n3 and B=p1q1r1p2q2r2p3q3r3 pi, qi, ri are the cofactors of the elements li, mi, ni for i=1,2,3. If l1,m1,n1,l2,m2,n2 and l3,m3,n3 are the direction cosines of three mutually perpendicular lines, then p1,q1,r1,p2,q2,r2 and p3,q3,r3 are
MEDIUM
JEE Advanced
IMPORTANT
If ABCD is a tetrahedron such that each ABC,ABD and ACD has a right angle at A. If arABC=K1arABD=K2 and arBCD=K3, then arACD is
HARD
JEE Advanced
IMPORTANT
In a regular tetrahedron, if the distance between the midpoints of opposite edges is unity, then its volume is
MEDIUM
JEE Advanced
IMPORTANT
A variable plane makes intercepts on X,Y and Z-axes and it makes a tetrahedron of volume 64 cu. The locus of foot of perpendicular from origin on this plane is
MEDIUM
JEE Advanced
IMPORTANT
If  P,Q,R,S are four coplanar points on the sides AB,BC,CD,DA of a skew quadrilateral, then APPB·BQQC·CRRD·DSSA equals
MEDIUM
JEE Advanced
IMPORTANT
Given the equations of the line 3xy+z+1=0 & 5 x+y+3 z=0. Then which of the following is correct?