Vector Cross product visualization

[Eli]

The cross product of vectors $\boldsymbol{u}$ and \( \boldsymbol{v} \) is a vector perpendicular to the plane containing them. In the applet below by Guillermo Bautista, the vector perpendicular to the plane is represented by vector \(\boldsymbol{w}\). However, the magnitude of vector \(\boldsymbol{w} \) is equal to the area of the parallelogram with sides \(\boldsymbol{u}\) and \(\boldsymbol{v}\). Drag points $A$ and $B$ to change the length and the direction of vectors \(\boldsymbol{u}\) and \(\boldsymbol{v}\).

See further examples below.


Example 1(By Dave Nero):

Example 2 (Authored by Kara Babcock, Wolfe Wall):

Example 3 (Authored by Mr Sexton):

Example 4 (Authored by Peter Johnston):