On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest to the origin. What is a+b+c?
On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest to the origin. What is a+b+c?
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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![**Question 5**
On the line of intersection of the planes \( y + 2z = 12 \) and \( x + y = 6 \), find the point \( (a, b, c) \) that is closest to the origin. What is \( a + b + c \)?
![3D Graph Explanation]
- The graph shows the intersection of two planes in a three-dimensional space.
- The red plane represents the equation \( y + 2z = 12 \).
- The green plane represents the equation \( x + y = 6 \).
- The blue diamond marks the origin (0,0,0) in the xyz-coordinate space.
- The line of intersection appears where the two planes meet.
**Options:**
Select one:
- a. 10
- b. 5
- c. 3
- d. 4
- e. 8](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F50589fea-07bb-4f50-a34c-95e031a700c5%2F21fdcf01-01f9-4044-8b21-62b743472ca2%2Fpzmrrii_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5**
On the line of intersection of the planes \( y + 2z = 12 \) and \( x + y = 6 \), find the point \( (a, b, c) \) that is closest to the origin. What is \( a + b + c \)?
![3D Graph Explanation]
- The graph shows the intersection of two planes in a three-dimensional space.
- The red plane represents the equation \( y + 2z = 12 \).
- The green plane represents the equation \( x + y = 6 \).
- The blue diamond marks the origin (0,0,0) in the xyz-coordinate space.
- The line of intersection appears where the two planes meet.
**Options:**
Select one:
- a. 10
- b. 5
- c. 3
- d. 4
- e. 8
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