91Ó°ÊÓ

Prove that the locus of a point, the sum of whose distances from the points \((a, 0,0)\) and \((-a, 0,0)\) is a constant \(2 k\), is the curve \(\frac{x^{2}}{t^{2}}+\frac{y^{2}+z^{2}}{t^{2}-1}=1\).

What are the direction cosines of the line which is equally inclined to the axes?

Prove by direction cosines the points \((1,-2,3),(2,3,-4)\) and \((0,-7,10)\) are collinear.

If in a tetrahedron the sum of the squares of opposite edges is equal, show that its pairs of opposite sides are at right angles.