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Find a point on the plane x + y z = 1 closest to the point (1, 6, -6). Also find the distance from this point to the plane. (a) We would like to minimize the distance of a point with coordinates (x, y, z) to the point (1,6, -6). In order to make it easier to take partial derivatives, let's minimize the squared distance instead. Let f(x, y, z) be the squared distance from (x, y, z) to (1,6, −6) in terms of x, y, z. f(x, y, z) = == f (b) Let g(x, y, z) = x + y − z − 1. Find the gradients ▼ƒ and Vg. Vf(x, y, z) = - , , Vg(x, y, z) = = , , (c) Find the point on the given plane closest to (1,6, —6). Enter answers as integers or fractions, no decimals. Point: (d) Find the distance from the point (1, 6, -6) to the plane. Enter an exact answer. Distance:

Find a point on the plane x + y z = 1 closest to the point (1, 6, -6). Also find the distance from this point to the plane. (a) We would like to minimize the distance of a point with coordinates (x, y, z) to the point (1,6, -6). In order to make it easier to take partial derivatives, let's minimize the squared distance instead. Let f(x, y, z) be the squared distance from (x, y, z) to (1,6, −6) in terms of x, y, z. f(x, y, z) = == f (b) Let g(x, y, z) = x + y − z − 1. Find the gradients ▼ƒ and Vg. Vf(x, y, z) = - , , Vg(x, y, z) = = , , (c) Find the point on the given plane closest to (1,6, —6). Enter answers as integers or fractions, no decimals. Point: (d) Find the distance from the point (1, 6, -6) to the plane. Enter an exact answer. Distance:

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 93E
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Find a point on the plane x + y z = 1 closest to the point (1, 6, -6). Also find the distance from this point to the plane. (a) We would like to minimize the distance of a point with coordinates (x, y, z) to the point (1,6, -6). In order to make it easier to take partial derivatives, let's minimize the squared distance instead. Let f(x, y, z) be the squared distance from (x, y, z) to (1,6, −6) in terms of x, y, z. f(x, y, z) = == f (b) Let g(x, y, z) = x + y − z − 1. Find the gradients ▼ƒ and Vg. Vf(x, y, z) = - , , Vg(x, y, z) = = , , (c) Find the point on the given plane closest to (1,6, —6). Enter answers as integers or fractions, no decimals. Point: (d) Find the distance from the point (1, 6, -6) to the plane. Enter an exact answer. Distance:
Transcribed Image Text:Find a point on the plane x + y z = 1 closest to the point (1, 6, -6). Also find the distance from this point to the plane. (a) We would like to minimize the distance of a point with coordinates (x, y, z) to the point (1,6, -6). In order to make it easier to take partial derivatives, let's minimize the squared distance instead. Let f(x, y, z) be the squared distance from (x, y, z) to (1,6, −6) in terms of x, y, z. f(x, y, z) = == f (b) Let g(x, y, z) = x + y − z − 1. Find the gradients ▼ƒ and Vg. Vf(x, y, z) = - , , Vg(x, y, z) = = , , (c) Find the point on the given plane closest to (1,6, —6). Enter answers as integers or fractions, no decimals. Point: (d) Find the distance from the point (1, 6, -6) to the plane. Enter an exact answer. Distance:
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