Vector Methods To Find An Area

Hello,



after searching around on the internet about this problem, it looks like it is Cramer's rule that I want to use, though it wasn't shown to us under that name.



My textbook doesn't cover the material required for this problem, so i'd really like to run what I have done past you guys :)



1. The problem statement, all variables and given/known data



The triangle ABC has vertices A(-1,3,0), B(-3,0,7), C(-1,2,3). Find AB, AC, CB.



Find also the area of the triangle, using a vector method.



2. Relevant equations







3. The attempt at a solution



I found the vectors easily enough.



AB = -2i - 3j + 7k



AC = -j + 3k



CB = -2i - 2j + 4k



Area of a triangle = 1/2 base x height



[itex]A[/itex] = [itex]( \frac{1}{2})[/itex] (AB x AC)



I don't know how to make matrices in latex, but I use what looks to me like cramer's rule (we were just told how to do it, as we haven't covered determinants yet) and come to an answer that;



A = -i + 3j + K



I hope it's clear to you, but if not, if you can show me how to display matrices i'll gladly show the working.



Thanks!