The points and are opposite ends of a diameter of a sphere.
MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Three-Dimensional Geometry · Introduction to Three-Dimensional Geometry
Problem
The points A(2,−1,4) and B(6,3,−2) are opposite ends of a diameter of a sphere.
(i) Find the coordinates of the centre of the sphere.
(ii) Calculate the length of its radius.
(iii) Obtain the equation of the sphere in standard form.
(iv) Determine whether the point P(5,1,1) lies on, inside or outside the sphere, giving reasons.