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Say, a and b are two vectors. Their components along the x & y axes are: ax, ay and bx, by.
So, a = i ax + j ay
and, b = i bx + j by
The magnitude of their cross product is defined by:
|a x b| = |a|.|b|.sin(p) where p is the angle between a and b.
My question is this: what is the most elegant proof for:
|a x b| = ax.by - ay.bx
This is trivial to show if the distributive property of cross product is used, which I don't know how to prove.
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