Problem 6. (The cross product project). The cross product for vectors in V is not associative, so some alternative way of handling expressions like a x (b x c) is sorely needed. We're going to prove the most common one here, in a few simple steps. Please review the material on the cross product in the notes ("Vectors in space", "Rotations in space", particularly the ezercises). If you use facts about the cross product from elsewhere I will count the whole problem as 0. 1. Explain why a x (b × c) must be a linear combination of b and c. 2. Under what conditions is yb+ốc perpendicular to a? What does this say about the coefficients of b and e in the linear combination a x (b x c) = _b+ _c? 3. Explain why if u and v are perpendicular, u x v = uv.
Problem 6. (The cross product project). The cross product for vectors in V is not associative, so some alternative way of handling expressions like a x (b x c) is sorely needed. We're going to prove the most common one here, in a few simple steps. Please review the material on the cross product in the notes ("Vectors in space", "Rotations in space", particularly the ezercises). If you use facts about the cross product from elsewhere I will count the whole problem as 0. 1. Explain why a x (b × c) must be a linear combination of b and c. 2. Under what conditions is yb+ốc perpendicular to a? What does this say about the coefficients of b and e in the linear combination a x (b x c) = _b+ _c? 3. Explain why if u and v are perpendicular, u x v = uv.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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