3D Visualization of vector calculus

This simulation visualizes the basic vector operations in 3D. Activating the button new vectors generates vectors of random orientation, drawn as blue arrows. For better clarity all arrows have an absolute value (length) of 1 and start at the magenta colored origin. They are embedded into a sphere of radius 1, that is shown as a transparent mesh.

At the start two vectors will be visible, a with red filling color of the arrowhead, b with white color.

At the left side one can chose among different perspective projections by radio buttons:

perspective: 3D projection with perspective distortion. It can be rotated with the mouse.

xy-projection: top view of the xy-plane (along the z-axis)

yz-projection: along the x-axis

xz-projection: along the y-axis

no perspective: 3D projection without distortion. It can be rotated with the mouse.

At the bottom the following data are shown for the 2 vectors a and b

Intersecting angle: in degrees.

Product of absolute values: always 1, as both are of length 1.

Scalar product: a∙b = a| |b| cos(a|b), with a|b the intersecting angle.

Absolute value of the vector product: |a x b| = |a| |b| sin(a|b).

At the top the following operations can be activated by check boxes:

Addition: a + b.

Subtraction: a - b.

Subtraction: b - a (= -(a - b)).

Vector product: a x b.

Vector product: b x a (= - a x b).

3 Vectors a + b + c: generation of c and sum (c with yellow filling color).

The chosen combination is maintained when new vectors are generated.