段階的に解決し、人工知能を使用せず、優れた仕事を行いますご支援ありがとうございましたSOLVE STEP BY STEP IN DIGITAL FORMATDON'T USE AI | DON'T USE AI I DON'T USE AI | DON'T USE AI |5. Find the minimum distance between the point (1,3, 2) and the planex+y+z=1. How much is that minimum distance worth?

Answered: 5. Find the minimum distance between…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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段階的に解決し、人工知能を使用せず、優れた仕事を行います
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SOLVE STEP BY STEP IN DIGITAL FORMAT
DON'T USE AI | DON'T USE AI I DON'T USE AI | DON'T USE AI |
5. Find the minimum distance between the point (1,3, 2) and the plane
x+y+z=1. How much is that minimum distance worth?

Expert Solution

Step 1: step 1

First we find the direction vector of the normal line to the plane. The normal vector is a vector that is perpendicular to the plane. In this case, the normal vector is (1,1,1).

Then we find the equation of the line that passes through the point (1,3,2) and has the direction vector (1,1,1). This line can be represented by the following parametric equation:

$x = 1 + t$

$y = 3 + t$

$z = 2 + t$

Now we find the point on the line that is closest to the plane. To do this, we can set the equation of the line equal to the equation of the plane and solve for t.

$1 + t + 3 + t + 2 + t = 1$