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Chapter 1: Vectors, Lines and Planes
Section 1.5: Applications of Vector Products
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Example 1.5.3
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Use the appropriate formula from Table 1.5.1 to calculate the area of the parallelogram whose vertices are the four points P:, Q:, R:, and S:.
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Solution
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Mathematical Solution
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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
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= =
and
= =
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Figure 1.5.3(a) Parallelogram PQRS
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The area of the parallelogram is then the magnitude of
= =
easily seen to be 160.
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Maple 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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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≻S
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By subtraction, obtain the vectors A and B along the edges of the parallelogram
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Context Panel: Assign Name
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Context Panel: Assign Name
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Obtain the area of the parallelogram as the norm of the cross product of A and B
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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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=
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Maple Solution - Coded
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Install the Student MultivariateCalculus package.
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Define the position vectors P, Q, and S.
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Obtain vectors A and B along the edges of the parallelogram.
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Compute the norm of the cross product of A and B.
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=
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