I want to calculate $\bigtriangleup$ ABC where $A(-2,-3,0)$,$B(-1,0,5)$,$C(4,2,2)$
What I did was to mark the triangle vertices randomly
1) calculate the middle of AB ( I call it G ) to find the vertical vector CG then what I do is to calculate $\frac{CG*AB}{2}$ but I dont get the right answer, this is the right way to do that? or I need to do something else?
thanks!
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Ofir Attia
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What does it mean to calculate $\triangle ABC$? – dtldarek Jul 19 '13 at 10:25
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Good link – Mikasa Jul 19 '13 at 10:27
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What do you want to calculate? – eccstartup Jul 19 '13 at 10:31
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the area of ABC – Ofir Attia Jul 19 '13 at 14:28
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If you want find $G$ so that $\vec{CG}\perp \vec{AB}$.
Set $\vec{OG}=t\vec{OA}+(1-t)\vec{OB}$,
then let $\vec{AG}\cdot{}\vec{CG}=0$.
You can solve $t$.
The area is $\frac{CG\cdot{}AB}{2}$.
eccstartup
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Use the cross product! $\|\vec u \times\vec v\|$ gives the area of the parallelogram spanned by $\vec u$ and $\vec v$. So $1/2$ times this gives the area of the triangle with vertices $\vec 0$, $\vec u$, and $\vec v$.
Ted Shifrin
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