Proving Law of Sines Using Vector Cross Product

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Homework Statement

Prove the law of sines using a vector cross product. (Hint, consider the area of the triangle and that A+B+C=0.)

Homework Equations

|A||C|sin ( θ ) = (a2c3 − a3c2) + (a3c1 − a1c3) + (a1c2 − a2c1)

The Attempt at a Solution

The farthest I went is to show .5 |a||c|sin \theta .. I've tried some other things but then it just turns out to be some incomprehensible mess. I chose C to be my longest side. I simply do not know what to do; I've exhausted both forms of the cross product I know, and it appers to go nowhere.

 

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Never mind, I figured it out. Thanks anyway!