For the following two (02) items: Suppose S is the sphere with the smallest radius that passes through the points A(1, 0, 0) , B(0, 1, 0) and C(0, 0, 1) . On which one of the following planes does the centre of S lie?

Step-by-step solution

The sphere S passes through the points A(1, 0, 0) , B(0, 1, 0) , and C(0, 0, 1) . The equation of the plane containing these three points is given by the intercept form: x 1 + y 1 + z 1 = 1 x + y + z - 1 = 0 Any sphere passing through A, B , and C will intersect this plane in a circle, which is the circumcircle of ABC . For the sphere to have the smallest possible radius, this circumcircle must be a great circle of the sphere. This means the centre of the sphere must lie exactly on the plane containing the points A