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Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. ax b = −b xa 2. (ca) x b = c(ax b) = ax (cb) 3. ax (b + c) = axb+ axc 4. (a + b) x c = axc + bxc 5. a (bx c) (axb).c . = 6. ax (bx c) = (a c)b - (ab)c Prove the property a x b = -bxa of the given theorem. Let a = (a₁, a₂, a₂) and b = (b₁, b₂, ba). Then we get the following. '1' axb- X - - = (-1) i(a₂b3-a₂b3) -j (a²b₁ — ª₁b²) + k(a₂b₁ — ª₁b₂) X

Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. ax b = −b xa 2. (ca) x b = c(ax b) = ax (cb) 3. ax (b + c) = axb+ axc 4. (a + b) x c = axc + bxc 5. a (bx c) (axb).c . = 6. ax (bx c) = (a c)b - (ab)c Prove the property a x b = -bxa of the given theorem. Let a = (a₁, a₂, a₂) and b = (b₁, b₂, ba). Then we get the following. '1' axb- X - - = (-1) i(a₂b3-a₂b3) -j (a²b₁ — ª₁b²) + k(a₂b₁ — ª₁b₂) X

Calculus: Early Transcendentals
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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Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. a x b = −b xa 2. (ca) x b = c(axb) = ax (cb) 3. ax (b + c) = ax b + axc 4. (a + b) x c = ax c + bxc 5. a (bx c) = (a x b) . c . 6. ax (bx c) = (a c)b - (a. b)c Prove the property a x b = -bxa of the given theorem. Let a = (a₁, a, a) and b (b₁, b₂, b3). Then we get the following. = axb= <a₂b-azb₂₁a₁b²-a3b₁₁a₁b₂-a₂b₁ > . X = (-1) i (a₂b3a₂b3) −j(ª3b₁ — α₁b³) +k(α₂b₁-ª₁b₂) - = -bxa. = X
Transcribed Image Text:Consider the following theorem. If a, b, and c are vectors and c is a scalar, then we have the following properties of the cross product. 1. a x b = −b xa 2. (ca) x b = c(axb) = ax (cb) 3. ax (b + c) = ax b + axc 4. (a + b) x c = ax c + bxc 5. a (bx c) = (a x b) . c . 6. ax (bx c) = (a c)b - (a. b)c Prove the property a x b = -bxa of the given theorem. Let a = (a₁, a, a) and b (b₁, b₂, b3). Then we get the following. = axb= <a₂b-azb₂₁a₁b²-a3b₁₁a₁b₂-a₂b₁ > . X = (-1) i (a₂b3a₂b3) −j(ª3b₁ — α₁b³) +k(α₂b₁-ª₁b₂) - = -bxa. = X
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