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Chapter 1: Vectors, Lines and Planes
Section 1.5: Applications of Vector Products
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Example 1.5.6
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Use the appropriate formula from Table 1.5.1 to calculate the distance of the point P: from the line through points Q: and R:.
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Solution
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Mathematical Solution
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The three points P, Q, and R necessarily lie in a plane. Using the colors green, black, and red, respectively, Figure 1.5.6(a) represents these three points in that plane.
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According to Table 1.5.1, the distance from P to the line through Q and R, is given by
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where
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Figure 1.5.6(a) Points P, Q, and R
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= = and = =
and P, Q, and R, are position vectors to points P, Q, and R, respectively. Vectors A and B appear in Figure 1.5.6(a) as the gray and gold vectors, respectively.
Since = = = , , and , the required distance is ≐ 5.09.
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Mathematical Solution - Interactive
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Initialize
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Tools≻Load Package: Student Multivariate Calculus
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Loading Student:-MultivariateCalculus
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Define the position vectors P, Q, and R
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Context Panel: Assign to a Name≻P
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Context Panel: Assign to a Name≻Q
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Context Panel: Assign to a Name≻R
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By subtraction, obtain the vectors A and B
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Context Panel: Assign Name
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Context Panel: Assign Name
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Apply the appropriate distance formula from Table 1.5.1
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Keyboard the norm bars.
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Common Symbols palette: Cross-product operator
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Context Panel: Evaluate and Display Inline
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Context Panel: Approximate≻5 (digits)
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=
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Mathematical Solution - Coded
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Install the Student MultivariateCalculus package.
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Define the position vectors P, Q, and R.
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Obtain the vectors A and B.
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Apply the evalf command to obtain a floating-point (decimal) approximation.
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