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4. Use the 3-space standard basis vectors to find three nonzero vectors a, b, c satisfying axb = a x c, where a × b 0 and b c. (This proves that the cross product operation does not have cancellation across equations.)

4. Use the 3-space standard basis vectors to find three nonzero vectors a, b, c satisfying axb = a x c, where a × b 0 and b c. (This proves that the cross product operation does not have cancellation across equations.)

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:** Use the 3-space standard basis vectors to find three nonzero vectors **a**, **b**, **c** satisfying **a** × **b** = **a** × **c**, where **a** × **b** ≠ 0 and **b** ≠ **c**. (This proves that the cross product operation does not have cancellation across equations.)
Transcribed Image Text:**Problem 4:** Use the 3-space standard basis vectors to find three nonzero vectors **a**, **b**, **c** satisfying **a** × **b** = **a** × **c**, where **a** × **b** ≠ 0 and **b** ≠ **c**. (This proves that the cross product operation does not have cancellation across equations.)
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