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**Unformatted text preview: **z component || u || = < 0, -2, 2> • it’s orthogonal to v and w • it has the right length: 2 Sqrt[2] u has positive z component Algebraic Properties Cross Product is NOT commutative! Algebraic Properties It is anti-commutative v x w = - w x v Algebraic Properties Anti-Commutative: because of right-hand rule v x w = - w x v Basic Unit Vectors i x j = k, j x k = i, k x i = j Algebraic Properties Cross Product is NOT associative! Algebraic Properties NOT associative! Example (i x i) x j ≠ i x (i x j) Algebraic Properties NOT associative! Example (i x i) x j ≠ i x (i x j) PROOF: (i x i) x j = 0 i x (i x j) = i x k = -j Important Fact ||v x w|| = area of parallelogram Important Fact ||u . (v x w)|| = volume of parallelepiped...

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