Chapter 1: Vectors, Lines and Planes
Section 1.5: Applications of Vector Products
Derive the formula given in Table 1.5.1 for the distance from a point to a line.
Figure 1.5.7(a) is obtained from Figure 1.5.6(a) by adding the angle θ between vectors A and B, and by adding the dotted red line from point P orthogonal to QR‾, the line through Q and R. The length of this dotted line is the distance from P to QR‾.
From Figure 1.5.7(a) and simple right-triangle trigonometry, d= B sinθ. But
so d=B∥A×B∥A B = A×B∥A∥
Figure 1.5.7(a) Distance from P to the line QR‾
<< Previous Example Section 1.5
Next Example >>
© Maplesoft, a division of Waterloo Maple Inc., 2021. 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
What kind of issue would you like to report? (Optional)