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‾
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