Question

Show that the points (3, 2, 2), (-1, 4, 2), (0, 5, 6), (2, 1, 2) lie on a sphere whose centre is (1, 3, 4). Find also its radius.

Answer 1

Here, $OA=\sqrt{(1-3{)}^2+(3-2{)}^2+(4-2{)}^2}$

=$\sqrt{4+1+4}$

=3 units

OB=$\sqrt{(1+1{)}^2+(3-1{)}^2+(4-3{)}^2}$

=$\sqrt{4+4+1}$

=3 units

OC=$\sqrt{(1-0{)}^2+(3-5{)}^2+(4-6{)}^2}$

=$\sqrt{1+4+4}$

=3 units

OD = $\sqrt{(1-2{)}^2+(3-1{)}^2+(4-2{)}^2}$

=$\sqrt{1+4+4}$

=3 units

Since, OA = OC = OD = OB, points A, B, C, D lie on a sphere with centre O.

Radius = 3units