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12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is |Ax¡ + By, + Cz – D| VA + B² + C² b. Find an equation for the sphere that is tangent to the planes x + y + z = 3 and x + y + z = 9 if the planes 2x – y = 0 and 3x – z = 0 pass through the center of the sphere.

12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is |Ax¡ + By, + Cz – D| VA + B² + C² b. Find an equation for the sphere that is tangent to the planes x + y + z = 3 and x + y + z = 9 if the planes 2x – y = 0 and 3x – z = 0 pass through the center of the sphere.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is |Ax¡ + By, + Cz – D| VA + B² + C² b. Find an equation for the sphere that is tangent to the planes x + y + z = 3 and x + y + z = 9 if the planes 2x – y = 0 and 3x – z = 0 pass through the center of the sphere.
Transcribed Image Text:12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is |Ax¡ + By, + Cz – D| VA + B² + C² b. Find an equation for the sphere that is tangent to the planes x + y + z = 3 and x + y + z = 9 if the planes 2x – y = 0 and 3x – z = 0 pass through the center of the sphere.
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