Use Problem 6a to prove that (|mathbf{a} times mathbf{b}|=a b sin theta). Data from Problem 6 Prove
Question:
Use Problem 6a to prove that \(|\mathbf{a} \times \mathbf{b}|=a b \sin \theta\).
Data from Problem 6
Prove the following vector identities:
a. \((\mathbf{a} \times \mathbf{b}) \cdot(\mathbf{c} \times \mathbf{d})=(\mathbf{a} \cdot \mathbf{c})(\mathbf{b} \cdot \mathbf{d})-(\mathbf{a} \cdot \mathbf{d})(\mathbf{b} \cdot \mathbf{c})\).
b. \((\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})=(\mathbf{a} \cdot \mathbf{b} \times \mathbf{d}) \mathbf{c}-(\mathbf{a} \cdot \mathbf{b} \times \mathbf{c}) \mathbf{d}\).
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Related Book For
A Course In Mathematical Methods For Physicists
ISBN: 9781138442085
1st Edition
Authors: Russell L Herman
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