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5. Let a and b be vectors in R³. (a) Prove that a xb is orthogonal to both a and b (Note: It's sufficient to show one of these, as the other follows from the exact same argument). (b) Prove the identity ||a x b||² = (a • a) (b •b) – (a · b)²

5. Let a and b be vectors in R³. (a) Prove that a xb is orthogonal to both a and b (Note: It's sufficient to show one of these, as the other follows from the exact same argument). (b) Prove the identity ||a x b||² = (a • a) (b •b) – (a · b)²

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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5. Let a and b be vectors in R°. (a) Prove that a x b is orthogonal to both a and b (Note: It's sufficient to show one of these, as the other follows from the exact same argument). (b) Prove the identity ||a x b||² = (a · a) (b•b) – (a · b)²
Transcribed Image Text:5. Let a and b be vectors in R°. (a) Prove that a x b is orthogonal to both a and b (Note: It's sufficient to show one of these, as the other follows from the exact same argument). (b) Prove the identity ||a x b||² = (a · a) (b•b) – (a · b)²
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