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2a + 6zy + 2y + 3z2 = 1. You are given that in canonical coordinates, the same surface is described by 5u- + 3u - uw = 1. The principal axes are in the directions of the vectors B1, B2 and B3. What are B1, B2 and B3? B1 B2 = 1B3 = 1 -2 B = ,B2 =1 ,B3 = B1 = 1 ,B2 = 4- B3 = -1 B = Bo = B3 =

2a + 6zy + 2y + 3z2 = 1. You are given that in canonical coordinates, the same surface is described by 5u- + 3u - uw = 1. The principal axes are in the directions of the vectors B1, B2 and B3. What are B1, B2 and B3? B1 B2 = 1B3 = 1 -2 B = ,B2 =1 ,B3 = B1 = 1 ,B2 = 4- B3 = -1 B = Bo = B3 =

Advanced Engineering Mathematics
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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Consider the quadric surface described by 2a + 6xy + 2y + 3z2 = 1. You are given that in canonical coordinates, the same surface is described by 5u? + 3u - w = 1. The principal axes are in the directions of the vectors B1, B2 and B3. What are B1, Bg and B3? () -()--() 1 B1 = 1 ,B2 = B3 = 1 B1 = B2 = B3 = B1 = B2 = -1 ,B3 = B1 = B2 = B3 = 08:12 None of these is correct.
Transcribed Image Text:Consider the quadric surface described by 2a + 6xy + 2y + 3z2 = 1. You are given that in canonical coordinates, the same surface is described by 5u? + 3u - w = 1. The principal axes are in the directions of the vectors B1, B2 and B3. What are B1, Bg and B3? () -()--() 1 B1 = 1 ,B2 = B3 = 1 B1 = B2 = B3 = B1 = B2 = -1 ,B3 = B1 = B2 = B3 = 08:12 None of these is correct.
Expert Solution
Step 1

The given surface 2x2+6xy+2y2+3z2=1 can be written as

1=x y z230320003xyz

Let A=230320003

In canonical coordinates , the surface 2x2+6xy+2y2+3z2=1 can be described as 5u2+3v2-w2=1. So, the eigen values of the matrix A are λ1=5, λ2=3, λ3=-1

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