The base vectors e; span a three-dimensional space (indices =1, 2 or 3) as shown in the sketch. This is a non-standard coordinate system in which the magnitudes of e, and ez are both 1, but the magnitude of e2 is 2. Also, the angle between e and ę is a/4. The angle between ez and both ei and e2 is a/2. A vector y referred to this basis is given by y = lęj + 1ę2 + 2ę3 a) b) c) Evaluate each of the nine possible values of gij Calculate y · v = Compute y · ę2and use this result to determine the angle between ęzand y
The base vectors e; span a three-dimensional space (indices =1, 2 or 3) as shown in the sketch. This is a non-standard coordinate system in which the magnitudes of e, and ez are both 1, but the magnitude of e2 is 2. Also, the angle between e and ę is a/4. The angle between ez and both ei and e2 is a/2. A vector y referred to this basis is given by y = lęj + 1ę2 + 2ę3 a) b) c) Evaluate each of the nine possible values of gij Calculate y · v = Compute y · ę2and use this result to determine the angle between ęzand y
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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![The base vectors e; span a three-dimensional space (indices = 1, 2 or 3) as shown in the sketch.
This is a non-standard coordinate system in which the magnitudes of e, and ez are both 1, but the
magnitude of e2 is 2. Also, the angle between e, and ezis a/4. The angle between ez and both
e, and e, is a/2. A vector y referred to this basis is given by y = 1e, + 1ę2 + 2ę3
e2
e1
Evaluate each of the nine possible values of gij
Calculate y · y = \y]<
Compute y · e2and use this result to determine the angle between ezand y](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bf5b396-9574-41e2-95d5-e23e6c84d38c%2F4cd20d4f-2f98-4a43-9420-abeb34367418%2F1hb9gti_processed.png&w=3840&q=75)
Transcribed Image Text:The base vectors e; span a three-dimensional space (indices = 1, 2 or 3) as shown in the sketch.
This is a non-standard coordinate system in which the magnitudes of e, and ez are both 1, but the
magnitude of e2 is 2. Also, the angle between e, and ezis a/4. The angle between ez and both
e, and e, is a/2. A vector y referred to this basis is given by y = 1e, + 1ę2 + 2ę3
e2
e1
Evaluate each of the nine possible values of gij
Calculate y · y = \y]<
Compute y · e2and use this result to determine the angle between ezand y
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