Mathematica Demos
Vector Products
You can move the vectors around to see how the two vector products change. When is the dot product zero? When is the cross product zero?
Note that I had to "fake" the cross product here. Cross products can only be computed for 3-dimensional vectors. So, for 2-dimensional vectors u=⟨ u1, u2 ⟩ and v=⟨ v1, v2 ⟩, I computed the cross product ⟨ u1, u2, 0 ⟩ × ⟨ v1, v2 , 0 ⟩ .
Vector Equation of a Line
Move around the initial position r0 and the direction v to see how the line r(t) = r0 + t v changes. You can move around the slider to see the position of a single particle at a specific time t.