Student[MultivariateCalculus] Examples - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

Home : Support : Online Help : Applications and Example Worksheets : Calculus : Student[MultivariateCalculus] Examples

Student MultivariateCalculus Examples

The Student:-MultivariateCalculus package is designed to aid in the teaching and understanding of multivariate calculus concepts.  For a general overview, see MultivariateCalculus.  For introductory examples, see MultivariateCalculus Example Worksheet.

Lines and Planes



Tools≻Load Package: Student Multivariate Calculus


Example 1: Equation of a Plane

Obtain the equation of the plane containing the three points 1,2,3, 1,3,1, 2,1,1.


Write a sequence of the three points.


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Plane
In the "Choose Variables for Plane" dialog, accept default names or provide new ones.


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Representation

1,2,3,1,3,1,2,1,1make planeStudent:-MultivariateCalculus:-Plane6101,1,2,3,variables=x,y,z,id=1representation6x10y+z=−23

Example 2: Skew Lines

Show that x=1+2 t,y=23 t,z=3+5 t and x=3s,y=5+3,z=7+6 s define skew lines, and find the distance between them.

Create Line Objects for each line


Form a list of the parametric equations defining a line.


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Line≻t or s, as appropriate


Context Panel: Assign to a Name≻L1 (or L2, as appropriate)

x=1+2 t,y=23 t,z=3+5 tmake lineStudent:-MultivariateCalculus:-Line1,2,3,235,variables=x,y,z,parameter=t,id=1assign to a nameL1

x=3s,y=5+3,z=7+6 smake lineStudent:-MultivariateCalculus:-Line3,8,7,106,variables=x,y,z,parameter=s,id=2assign to a nameL2

Verify the lines are skew


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Skew (or Parallel or Intersects)

L1,L2skew lines?true



Obtain the distance between the lines


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Distance


Context Panel: Approximate≻10 (digits)

L1,L2distance75622311at 10 digits6.014452050

The standard approach to finding the distance between skew lines is vectorial: Obtain N, the vector orthogonal to both lines, and project V, any vector from one line to the other, onto N. The length of this projection is the distance between the lines.

Obtain N, the common normal


Context Panel: Student Multivariate Calculus≻Lines & Planes≻Direction


Context Panel: Assign to a Name≻V1 (or V2, as applicable)

L1direction235assign to a nameV1