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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 48E
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