Desmos Calculators allow you to visualize vector operations on points. In Desmos 3D and the Geometry tool, you can graph vectors by typing vector\((a,b)\) with starting point \(a\) and terminal point \(b\). For example, vector\(((0,0,0),(3,3,3))\) will graph a 3D vector in standard position with terminal point \((3,3,3)\).
Operations on Points and Vectors
You can also perform operations with points and vectors! Point operations work in the Graphing Calculator, Geometry Tool, and 3D Calculator. Vector operations are currently only supported in the Geometry Tool and 3D Calculator.
In the following table, \(a\) and \(b\) represent points and \(v_1\) and \(v_2\) represent vectors. You can explore these operations in the Vector and Point Operations in 3D example graph.
| Function: | This function... |
|---|---|
| \(a.x, a.y, a.z\) | outputs the x, y, and z component of your point (numerical). |
| \(v_1\).start | plots the initial point of your vector. |
| \(v_2\).end | plots the terminal point of your vector. |
| \(|a|\) or \(|v|\) | outputs the magnitude of your vector. On a point, it outputs the magnitude of the vector in standard position to point a (numerical). |
| \(a + b\) or \(v_1+v_2\) | graphs the vector sum of two points or vectors. |
| \(a - b\) or \(v_1-v_2\) | graphs the vector difference of two points or vectors. |
| \(ka\) or \(kv\) | graphs the scalar multiple of a constant, k, times a point or vector. |
| \(v_1\)\(\cdot\)\(v_2\) | outputs the scalar value that results when you multiply two vectors. This is found by multiplying the x components, y components, and z components (in 3D) and then summing the results (numerical). |
| \(v_1\)\(\times\)\(v_2\) | graphs the vector perpendicular to the plane containing the original two vectors. The cross product is only defined in 3D. To get the \(\times\) symbol, type the word cross. |
3D Vector Videos
Learn more about vectors through our #Unlocking3D videos series:
Learn More
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