Area of Triangle: Solving 1/2 |( BxC + CxA + AxB )|

[jesuslovesu]

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?

 

[rock.freak667]

For a triangle of side |a| and |b| with included angle , what does \frac{1}{2} |a||b|sin\alpha give?

 

[tiny-tim]

Hi jesuslovesu!

Hint: what is the area of triangle OAB?