Example 1-4-1 - Maple Help

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Chapter 1: Vectors, Lines and Planes



Section 1.4: Cross Product



Example 1.4.1



For the vectors  and , and the scalar $c$,

 a) Obtain $\mathbf{A}×\mathbf{B}$.
 b) Obtain $\mathrm{θ}$, the angle between A and B.
 c) Verify computationally that $\mathbf{A}×\mathbf{A}=\mathbf{0}$.
 d) Verify computationally that .
 e) Verify computationally that .
 f) Verify that both A and B are perpendicular to $\mathbf{A}×\mathbf{B}$.
 g) Verify that ${\left(\mathbf{A}·\mathbf{B}\right)}^{2}+{∥\mathbf{A}×\mathbf{B}∥}^{2}$ = .
 h) Verify that ${\left(\mathbf{A}·\mathbf{B}\right)}^{2}-{∥\mathbf{A}×\mathbf{B}∥}^{2}$ = .
 i) Show that $\mathbf{A}×\left(\mathbf{A}×\mathbf{B}\right)\ne \left(\mathbf{A}×\mathbf{A}\right)×\mathbf{B}=\mathbf{0}$.
 j) Verify that .
 k) Verify that $\left(\mathbf{A}-\mathbf{B}\right)×\left(\mathbf{A}+\mathbf{B}\right)=2\left(\mathbf{A}×\mathbf{B}\right)$.