Chapter 1: Vectors, Lines and Planes
Section 1.5: Applications of Vector Products
Use the appropriate formula from Table 1.5.1 to calculate the area of the parallelogram whose vertices are the four points P:4,13, Q:12,29, R:16,57, and S:8,41.
Figure 1.5.3(a) shows the parallelogram formed by the points P, Q, R, and S. If P, Q, and S are position vectors to the points P, Q, and S, then two adjacent edges of the parallelogram are described by the vectors
A=Q−P = 12290−4130 = 8160
B=S−P = 8410−4130 = 4280
Figure 1.5.3(a) Parallelogram PQRS
The area of the parallelogram is then the magnitude of
A×B= |ijk81604280| = 008⋅28−4⋅16 = 00160
easily seen to be 160.
Maple Solution - Interactive
Tools≻Load Package: Student Multivariate Calculus
Enter P as per Table 1.1.1.
Context Panel: Assign to a Name≻P
4,13,0→assign to a nameP
Enter Q as per Table 1.1.1.
Context Panel: Assign to a Name≻Q
12,29,0→assign to a nameQ
Enter S as per Table 1.1.1.
Context Panel: Assign to a Name≻S
8,41,0→assign to a nameS
By subtraction, obtain the vectors A and B along the edges of the parallelogram
Context Panel: Assign Name
Obtain the area of the parallelogram as the norm of the cross product of A and B
Keyboard the norm bars.
Common Symbols palette: Cross-product operator
Context Panel: Evaluate and Display Inline
A×B = 160
Maple Solution - Coded
Install the Student MultivariateCalculus package.
Define the position vectors P, Q, and S.
Obtain vectors A and B along the edges of the parallelogram.
Compute the norm of the cross product of A and B.
NormCrossProductA,B = 160
<< Previous Example Section 1.5
Next Example >>
© 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
Download Help Document