A sphere of constant radius r through the origin intersects the coordinate axes in A, B and C. What is the locus of the centroid of the $$\Delta$$ABC ?

The coordinates of the vertices P, Q and R of a triangle PQR are (1, $$-$$1, 1), (3, $$-$$2, 2) and (0, 2, 6) respectively. If $$\angle$$RQP = $$\theta$$, then what is $$\angle$$PRQ equal to?

If the line $${{x - 4} \over 1} = {{y - 2} \over 1} = {{z - k} \over 2}$$ lies on the plane $$2x - 4y + z = 7$$, then what is the value of k?

A point on the line $${{x - 1} \over 1} = {{y - 3} \over 2} = {{z + 2} \over 7}$$ has coordinates