Let c be a number, and let a and b be vectors in R³. Let x = (x, y, z). Show that the equation (x− a) · (x − b) = c² defines a sphere with centre whose position vector is (a+b) and radius [c² + (a-b)|²].

Let c be a number, and let a and b be vectors in R³. Let x = (x, y, z). Show that the equation (x− a) · (x − b) = c² defines a sphere with centre whose position vector is (a+b) and radius [c² + (a-b)|²].

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.1: Length And Dot Product In R^n

Problem 17E: Consider the vector v=(1,3,0,4). Find u such that a u has the same direction as v and one-half of...

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Question

Let c be a number, and let a and b be vectors in R³. Let x = (x, y, z). Show that the equation
(x− a) · (x− b) = c² defines a sphere with centre whose position vector is ½(a + b) and radius
[c² +|½/(a−b)|²] ¾.

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