Question

Let (3, 4, –1) and (–1, 2, 3) be the end points of a diameter of a sphere. Then, the radius of the sphere is equal to
(a) 2
(b) 3
(c) 6
(d) 7

Answer 1

(b) 3

Suppose d is the diameter of the sphere. Then

$$\begin{gathered} d^2={\left(-1-3\right)}^2+{\left(2-4\right)}^2+{\left(3+1\right)}^2 \\ \Rightarrow d^2={\left(-4\right)}^2+{\left(-2\right)}^2+{\left(4\right)}^2 \\ \Rightarrow d^2=16+4+16 \\ \Rightarrow d^2=36 \\ \Rightarrow d=6 \end{gathered}$$

Hence, radius of the sphere is 3 units.