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Three proofs Prove that u × u = 0 in three ways.a. Use the
Chapter 10, Problem 60AE(choose chapter or problem)
\(\mathbf{u} \times \mathbf{u}\) Prove that \(\mathbf{u} \times \mathbf{u}\) = 0 in three ways.
a. Use the definition of the cross product.
b. Use the determinant formulation of the cross product.
c. Use the property that \(\mathbf{u} \times \mathbf{v}=-(\mathbf{v} \times \mathbf{u})\).
Questions & Answers
QUESTION:
\(\mathbf{u} \times \mathbf{u}\) Prove that \(\mathbf{u} \times \mathbf{u}\) = 0 in three ways.
a. Use the definition of the cross product.
b. Use the determinant formulation of the cross product.
c. Use the property that \(\mathbf{u} \times \mathbf{v}=-(\mathbf{v} \times \mathbf{u})\).
ANSWER:Solution 60AEStep 1 of 3:In this problem we need to prove u × u = 0 in three ways.a. Use the definition of the cross product.Definition of cross product:Given vectors u and v, the cross product of u and v is the vector Since here the only vector is u and we know that the angle between a vector and itself is 0 we get Now using definition of cross product we get,(since sin 0=0)Hence u × u = 0