Use Exercises 1 and 2 to show that if is a point on the sphere x2 + y2 + z2 = r2, then th...

Use Exercises 1 and 2 to show that if is a point on the sphere x2 + y2 + z2 = r2, then the equation for the plane tangent to the sphere at is

Exercises 1–2

1. The set of points in ℝ3 that are equidistant from two given points A = (a1, a2, a3) and B = (b1, b2, b3) is a plane. Show that the equation for this plane is

where is the midpoint of the segment AB.

2. Suppose that the midpoint and one endpoint of a segment are known. Find the other endpoint in terms of the two known points.