Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Example 1.1.2
Calculate the magnitude of the position vector to the point 1,2.
Solution
Mathematical Solution
From Figure 1.1.1 and the recipe V=a2+b2, the magnitude (or length) of the given position vector is 12+22=5.
Maple Solution - Interactive
With Student MultivariateCalculus, (or LinearAlgebra, or VectorCalculus) loaded, the norm defaults to the Euclidean norm. This norm in the Student MultivariateCalculus package can be accessed either from the Context Panel, or directly, with Typeset math.
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Write the vector as per Table 1.1.1. Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Norm
1,2 = →norm5
Write with Typeset math. Context Panel: Evaluate and Display Inline
1,2 = 5
Here are two top-level solutions (no packages installed).
Solution via Context Panel
Enter the vector as per Table 1.1.1. Press the Enter key.
Context Panel: Norm≻Euclidean
1,2
→Euclidean-norm
5
Solution via 2D math notation
Type two vertical strokes on either side of the given position vector, the append the subscript 2.
Context Panel: Evaluate and Display Inline
1,22 = 5
The subscript on the norm forces Maple to compute the 2-norm, that is, the Euclidean norm. At top level, with no relevant package loaded, Maple's norm (computed via Typeset math notation) is the largest absolute value of the components, the default for the LinearAlgebra package.
Maple Solution - Coded
The Norm command exists only in certain packages. Hence, at top level, without one of those packages being loaded, the Norm command returns unevaluated. Within the LinearAlgebra package, the Norm command defaults to the infinity norm, the largest absolute value of the components. To obtain the Euclidean norm in the LinearAlgebra package, an additional parameter (either "2" or "Euclidean") must be added. In the Student MultivariateCalculus, LinearAlgebra and VectorCalculus packages, Norm defaults to the Euclidean norm.
No relevant package loaded
Apply the Norm command.
Norm1,2
With the Student MultivariateCalculus package installed
Install the Student MultivariateCalculus package.
withStudent:-MultivariateCalculus:
Norm1,2 = 5
Options within the LinearAlgebra package
Install the LinearAlgebra package.
withLinearAlgebra:
Apply the Norm command. Note the return of the infinity norm, not the Euclidean (or 2-norm).
Norm1 ,2
2
Apply the Norm command with the additional parameter "2" to designate the 2-norm.
Norm1,2,2
Compare to the behavior under the Student LinearAlgebra package
Install the Student LinearAlgebra package.
withStudent:-LinearAlgebra:
Apply the Norm command, which, in the presence of the Student LinearAlgebra package, will now default to the Euclidean norm.
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