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Problem 4. The table of the direction cosines for two right-handed coordinate systems (,) are given below: 15 e₁e₂e3 1 √2-1 2 2 2 12 1 2 2 3 ??? Required: a. Determine a31, 032, and a33 assuming that coordinates ; form an othogonal reference system. b. From the results of Problem 4.a, show that the base vectors of the coordinate system ; are unit vectors and mutually perpendicular to each other. c. State the transformation relation between the two coordinates in the form x= x(). Is this reversible? Explain.

Problem 4. The table of the direction cosines for two right-handed coordinate systems (,) are given below: 15 e₁e₂e3 1 √2-1 2 2 2 12 1 2 2 3 ??? Required: a. Determine a31, 032, and a33 assuming that coordinates ; form an othogonal reference system. b. From the results of Problem 4.a, show that the base vectors of the coordinate system ; are unit vectors and mutually perpendicular to each other. c. State the transformation relation between the two coordinates in the form x= x(). Is this reversible? Explain.

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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Problem 4. The table of the direction cosines for two right-handed coordinate systems (₁, 2) are given below: e₁e₂e3 1 √2-1 2 √2 2 ē3 ??? ODI 1 2 1 2 Required: a. Determine a31, 032, and a33 assuming that coordinates ; form an othogonal reference system. b. From the results of Problem 4.a, show that the base vectors of the coordinate system ; are unit vectors and mutually perpendicular to each other. c. State the transformation relation between the two coordinates in the form x= x; (). Is this reversible? Explain.
Transcribed Image Text:Problem 4. The table of the direction cosines for two right-handed coordinate systems (₁, 2) are given below: e₁e₂e3 1 √2-1 2 √2 2 ē3 ??? ODI 1 2 1 2 Required: a. Determine a31, 032, and a33 assuming that coordinates ; form an othogonal reference system. b. From the results of Problem 4.a, show that the base vectors of the coordinate system ; are unit vectors and mutually perpendicular to each other. c. State the transformation relation between the two coordinates in the form x= x; (). Is this reversible? Explain.
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