Example 1-4-1 - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

# Online Help

###### All Products    Maple    MapleSim



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 $\left(\mathbf{A}-\mathbf{B}\right)×\left(\mathbf{A}+\mathbf{B}\right)=2\left(\mathbf{A}×\mathbf{B}\right)$.







© Maplesoft, a division of Waterloo Maple Inc., 2023. All rights reserved. This product is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation.



For more information on Maplesoft products and services, visit www.maplesoft.com