Chapter 1: Vectors, Lines and Planes
Section 1.1: Cartesian Coordinates and Vectors
Determine the angles α,β,γ, that the position vector to 1,2,3 makes with the x-, y-, and z-axes, respectively.
The three direction angles for a vector reside in the three right triangles in Figure 1.1.2. Their values, obtained by applying basic right-triangle trigonometry to these triangles where the hypotenuse is 1,2,3=14, are listed in Table 1.1.8(a).
Table 1.1.8(a) Direction angles for given vector
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 one of the axes.
Tools≻Load Package: Student Multivariate Calculus
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 appropriate coordinate-axis.
Context Panel: Evaluate and Display Inline
Context Panel: Student Multivariate Calculus≻Lines & Planes≻Angle
Context Panel: Approximate≻5 (digits)
1,2,3,1,0,0 = 123,100→anglearccos⁡114⁢14→at 5 digits1.3002
1,2,3,0,1,0 = 123,010→anglearccos⁡17⁢14→at 5 digits1.0068
1,2,3,0,0,1 = 123,001→anglearccos⁡314⁢14→at 5 digits0.64048
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 appropriate axis.
Student:-MultivariateCalculus:-Angle1,2,3,1,0,0 = arccos⁡114⁢14
Student:-MultivariateCalculus:-Angle1,2,3,0,1,0 = arccos⁡17⁢14
Student:-MultivariateCalculus:-Angle1,2,3,0,0,1 = arccos⁡314⁢14
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