# Thread: Finding the area of a triangle on the space given three points

1. ## Finding the area of a triangle on the space given three points

Hi there, I must solve the next problem. The sentence says:
Find the area of a triangle wich vertex are the points: $\displaystyle V_1(1,5,-2)$ $\displaystyle V_2(0,0,0)$ and $\displaystyle V_3(3,5,1)$.

What I did was define the vectors: $\displaystyle \vec{v_1}=(1,5,-2)$ y $\displaystyle \vec{v_3}=(3,5,1)$, considering the point $\displaystyle v_2$ is the origin, these vectors are $\displaystyle \vec{v_2v_1}$ y $\displaystyle \vec{v_2v_3}$.

So I took the vectors $\displaystyle \vec{v_1}$ and $\displaystyle \vec{v_3}$ and then what I did was getting the module of the vectorial product, which is the area of the parallelogram conformed by these two vectors, and then I've divide it on two:

$\displaystyle A=\displaystyle\frac{||v_1\wedge{v_3}||}{2}$

$\displaystyle v_1\wedge{v_3}=(15,-7,-10)\Rightarrow{||(15,-7,-10)||=\sqrt[ ]{347}}$

Then: $\displaystyle A=\displaystyle\frac{||v_1\wedge{v_3}||}{2}=\displ aystyle\frac{\sqrt[ ]{347}}{2}$

Is it right?

Bye, and thanks for commenting.

2. Originally Posted by Ulysses
Hi there, I must solve the next problem. The sentence says:
Find the area of a triangle wich vertex are the points: $\displaystyle V_1(1,5,-2)$ $\displaystyle V_2(0,0,0)$ and $\displaystyle V_3(3,5,1)$.

What I did was define the vectors: $\displaystyle \vec{v_1}=(1,5,-2)$ y $\displaystyle \vec{v_3}=(3,5,1)$, considering the point $\displaystyle v_2$ is the origin, these vectors are $\displaystyle \vec{v_2v_1}$ y $\displaystyle \vec{v_2v_3}$.

So I took the vectors $\displaystyle \vec{v_1}$ and $\displaystyle \vec{v_3}$ and then what I did was getting the module of the vectorial product, which is the area of the parallelogram conformed by these two vectors, and then I've divide it on two:

$\displaystyle A=\displaystyle\frac{||v_1\wedge{v_3}||}{2}$

$\displaystyle v_1\wedge{v_3}=(15,-7,-10)\Rightarrow{||(15,-7,-10)||=\sqrt[ ]{347}}$

Then: $\displaystyle A=\displaystyle\frac{||v_1\wedge{v_3}||}{2}=\displ aystyle\frac{\sqrt[ ]{347}}{2}$

Is it right?

Bye, and thanks for commenting.
$\displaystyle \frac{\sqrt{374}}{2}$

3. Thanks, didn't note that :P