MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry
Problem
A moving point P(t,2t,t+1) depends on the real parameter t.
(i) Obtain, in simplest form, an expression for the square of the distance of P from the origin in terms of t.
(ii) For what values of t does the point P lie strictly inside the sphere of radius 5 centred at the origin?
(iii) For what value(s) of t does P lie on the surface of the same sphere?