manjula

show that the locus of a point whose distances from two given planes are in a constant ratio, is a plane.

if in a tetrahedron the sums of the squares of opposite sides are equal,show that its pairs of opposite sides are right angles

if (l1,m1,n1),(l2,m2,n2),(l3,m3,n3) are the direction cosines of three mutual perpendicular lines,show that the line whose direction ratios area l1+l2+l3,m1+m2+m3,n1+n2+n3 make equal angles with them