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Area of a Triangle

  • #1
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Homework Statement



The three vectors A, B, C point from the origin O to the three corners of a triangle. Show that the area of a triangle = 1/2 |( BxC + CxA + AxB )|

Homework Equations



1/2 |a x b| = 1/2 |a||b|sin(alpha)


The Attempt at a Solution



My initial attempt at this problem was to take the cross product like (Bx, By, Bz) x (Cx, Cy, Cz) and seeing if anything canceled. Unfortunately nothing did (I also tried with a '2d' vector (Bx, By, 0) etc and nothing canceled either).


I believe I have to somehow use the equation I listed, but I'm not really sure what to do. It seems a little counterproductive to do the cross product three times. There aren't any simplifications that I can see. Anyone know where I should start?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
For a triangle of side |a| and |b| with included angle [itex], what does [itex]\frac{1}{2} |a||b|sin\alpha[/itex] give?
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,832
249
Hi jesuslovesu! :smile:

Hint: what is the area of triangle OAB? :smile:
 

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