Example 1-4-2 - Maple Help



Chapter 1: Vectors, Lines and Planes



Section 1.4: Cross Product



Example 1.4.2



For the vectors , , and ,

 a) Verify the distributive property $\mathbf{A}×\left(\mathbf{B}+\mathbf{C}\right)=\mathbf{A}×\mathbf{B}+\mathbf{A}×\mathbf{C}$.
 b) Verify the distributive property $\left(\mathbf{A}+\mathbf{B}\right)×\mathbf{C}=\mathbf{A}×\mathbf{C}+\mathbf{B}×\mathbf{C}$.
 c) Show that $\mathbf{A}×\left(\mathbf{B}×\mathbf{C}\right)\ne \left(\mathbf{A}×\mathbf{B}\right)×\mathbf{C}$.
 d) Verify the identity $\mathbf{A}×\left(\mathbf{B}×\mathbf{C}\right)+\mathbf{B}×\left(\mathbf{C}×\mathbf{A}\right)+\mathbf{C}×\left(\mathbf{A}×\mathbf{B}\right)=\mathbf{0}$.
 e) Verify the identity $\mathbf{A}×\left(\mathbf{B}×\mathbf{C}\right)=\left(\mathbf{A}·\mathbf{C}\right)\mathbf{B}-\left(\mathbf{A}·\mathbf{B}\right)\mathbf{C}$.
 f) Verify the identity $\left(\mathbf{A}×\mathbf{B}\right)×\mathbf{C}=\left(\mathbf{A}·\mathbf{C}\right)\mathbf{B}-\left(\mathbf{B}·\mathbf{C}\right)\mathbf{A}$.