Vectors and Desmos in 3D

Recently, I’ve been working with Desmos in 3D. It is easy to perform a number of vector operations:

• defining a vector in 3D
• multiplying a vector by a scalar
• magnitude of a vector
• dot product
• cross product
• graphs of vectors are shown in 3D in a rotatable cube
• learn more here: https://www.desmos.com/calculator/fk1xh0lgnn
• some of the applications described below have also been added to the link

I also did some work on algebraic computations with 3D vectors, creating functions in (original) Desmos used in the following applications:

• converting angles between radians and degrees
• computing vector magnitude
• adding 3D vectors (algebraically)
• dot product
• cross product
• area of parallelogram bounded by two vectors
• scalar projection
• vector projection
• angle of a vector to the x, y and z axes
• angle between two vectors
• learn more here: https://www.desmos.com/calculator/m9ac0d00qa
• 2D vectors may be manipulated using the 3D functions by setting the z components of vectors to zero

Thinking about the vectors curriculum in Grade 12 Calculus and Vectors, MCV4U, it may be a useful exercise for classroom teachers to have students create and use functions like these — operationalizing them to demonstrate their correct implementation and use.

Here is a useful video introducing 3D Desmos: