- #1
JizzaDaMan
- 48
- 0
Why is the cross product of two vectors perpendicular to the plane the two vectors lie on?
I am aware that you can prove this by showing that:
[itex](\vec{a}\times\vec{b})\cdot\vec{a} = (\vec{a}\times\vec{b})\cdot\vec{b} = 0[/itex]
Surely it was not defined as this and worked backwards though. I see little advantage in making this definition, and simply guessing it seems a bit random, so what brings it about?
I am aware that you can prove this by showing that:
[itex](\vec{a}\times\vec{b})\cdot\vec{a} = (\vec{a}\times\vec{b})\cdot\vec{b} = 0[/itex]
Surely it was not defined as this and worked backwards though. I see little advantage in making this definition, and simply guessing it seems a bit random, so what brings it about?