Mathematics

Problem

Two points in space are

A(k,1,2)

and

B(3,k,0)

, where

k

is a real parameter. a. (i) Find all real values of

k

for which the distances of

A

and

B

from the origin are equal. b. (ii) For each value of

k

obtained in part (i), calculate the common distance and state whether it is less than

4

, equal to

4

, or greater than

4

. c. (iii) Verify that, for the values of

k

found, the two points

A

and

B

lie on the same sphere centred at the origin and determine the radius of this sphere.