II1. Recall that using vector projections, we showed that the dis- tance from a point (x₁, y₁, 2₁) to a plane ax + by + cz + d = 0 is D |ax₁+by₁+cz₁+d Assuming that a, b, c are nonzero, give a different proof of this formula using Lagrange multipliers. √²+6²+c² =

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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II1. Recall that using vector projections, we showed that the dis-
tance from a point (x₁, y₁, 2₁) to a plane ax + by + cz + d = 0 is
Assuming that a, b, c are nonzero, give a
D
|axı+by₁+cz₁+d|
√a² +6² +c²
different proof of this formula using Lagrange multipliers.
=
Transcribed Image Text:II1. Recall that using vector projections, we showed that the dis- tance from a point (x₁, y₁, 2₁) to a plane ax + by + cz + d = 0 is Assuming that a, b, c are nonzero, give a D |axı+by₁+cz₁+d| √a² +6² +c² different proof of this formula using Lagrange multipliers. =
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