Chapter 1: Vectors, Lines and Planes
Section 1.3: Dot Product
Example 1.3.7
Use vector methods to find the distance between the points A:4,5,7 and B:−3,2,3.
Solution
Mathematical Solution
The distance from point B to point A is the magnitude (length) of the vector A−B given by the following calculation.
A−B = 457−−323 = ∥734∥ = 72+32+42=49+9+16=74
Maple Solution - Interactive
Initialize
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Enter A as per Table 1.1.1.
Context Panel: Assign Name
A=4,5,7→assign
Enter B as per Table 1.1.1.
B=−3,2,3→assign
Obtain A−B
Context Panel: Evaluate and Display Inline
A−B = 74
Alternatively, use the Context Panel
Write the difference of the two vectors. Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Norm
A−B = →norm74
The Distance option in the Student Precalculus package provides an alternative approach.
Tools≻Load Package: Student Precalculus
Loading Student:-Precalculus
Write the sequence of two vectors. Context Panel: Evaluate and Display Inline
Context Panel: Student Precalculus≻ Lines and segments≻Distance
A,B = →distance between points74
Table 1.3.7(a) provides a solution via the task template. Points can be entered either as lists or as vectors.
Tools≻Tasks≻Browse: Algebra≻Distance between Two Points
Distance between Two Real Points
Enter points as lists or vectors:
Point 1:
Point 2:
=
Table 1.3.7(a) Task template for finding distance between two points
Maple Solution - Coded
Install the Student MultivariateCalculus package.
withStudent:-MultivariateCalculus:
Assign the given vectors to the names A and B.
A,B≔4,5,7,−3,2,3:
Apply the Norm command.
NormA−B = 74
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