Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Example 1.1.4
Determine the angle that the position vector to 1,2 makes with the x-axis.
Solution
Mathematical Solution
From Figure 1.1.4(a), a graph of the given position vector, the angle θ is determined by simple right-triangle trigonometry.
tanθ=2/1
⇒θ=tan−12
cosθ=1/5
⇒θ=cos−11/5
sinθ=2/5
⇒θ=sin−12/5
θ≐1.107 radians or 63.4°
use plots, Student:-VectorCalculus in module() local p1,p2,p3,p4; p1:=PlotVector(<1,2>,color=black); p2:=plot([[[0,0],[1,0]],[[1,0],[1,2]]],style=line,linestyle=dot,color=red): p3:=textplot({[.5,.1,1],[.9,1,2],[.2,.1,typeset(theta)],[.55,.75,typeset(sqrt(5))]}); p4:=display(p1,p2,p3,scaling=constrained,axes=none); print(p4); end module: end use:
Figure 1.1.4(a) Right triangle formed by the given position vector and the horizontal
Maple Solution - Interactive
The Student MultivariateCalculus package provides the Angle command, which returns (in radians) the angle between two vectors. Use the Context Panel to apply this command to the given position vector and another position vector whose direction is that of the x-axis.
Tools≻Load Package: Student Multivariate Calculus
Loading Student:-MultivariateCalculus
Form a sequence of two vectors (see Table 1.1.1), one the given position vector, and the other any position vector whose direction is that of the x-axis.
Context Panel: Evaluate and Display Inline
Context Menu: Student Multivariate Calculus≻Lines & Planes≻Angle
1,2,1,0 = →anglearccos155
Maple Solution - Coded
Apply the Angle command in the Student MultivariateCalculus package to the given position vector and any other vector whose direction is that of the x-axis.
Install the Student MultivariateCalculus package.
withStudent:-MultivariateCalculus:
Apply the Angle command.
Angle1,2,1,0 = arccos155
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