# Thread: vector equation of plane

1. ## vector equation of plane

Hello.. I need help with vector equation!!!

Find the vector equation of the plane that passes through the points (1,2,7), (2,3,4) and (-1,2,1)

I know how to work out with the two pionts but not three

THANKYOU FOR HELPING ME = )

2. Originally Posted by sinni8
Hello.. I need help with vector equation!!!

Find the vector equation of the plane that passes through the points (1,2,7), (2,3,4) and (-1,2,1)
see example 1 here

I know how to work out with the two pionts but not three
no you don't ...it can't be done

and if you could, why didn't you just ignore the third point and do it?

3. Originally Posted by Jhevon
see example 1 here

no you don't ...it can't be done

and if you could, why didn't you just ignore the third point and do it?
No i cant what i mean is i can find the vector equation of plane with there are two points such as (1,2,1) and (2,3,5) but Since i have three points i need to the other method which is i cant do it!!

4. A plane can be defined as: $\displaystyle a(x - x_{0}) + b(y - y_{0}) + c(z - z_{0}) = 0$

where $\displaystyle (x_0, y_0, z_0)$ is a point on the plane and $\displaystyle (a,b,c)$ is the normal vector.

Let points A, B, C be (1,2,7), (2,3,4) and (-1,2,1) respectively.

Notice that the plane contains vectors $\displaystyle \overrightarrow{AB}$ and $\displaystyle \overrightarrow{AC}$ and their cross product will give the normal vector perpendicular to it.

So find $\displaystyle \overrightarrow{AB} \times \overrightarrow{AC}$ to get (a,b,c) and use one of A, B, or C for your $\displaystyle (x_{0}, y_0, z_0)$.

Now, again, plug it all into: $\displaystyle a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$

5. Originally Posted by sinni8
No i cant what i mean is i can find the vector equation of plane with there are two points such as (1,2,1) and (2,3,5) but Since i have three points i need to the other method which is i cant do it!!
you cannot, repeat, cannot find the vector equation of a plane if all you are given are two points in the plane. you need more information. see the link i gave you, it goes through a problem exactly like this one. take a gander at o_O's post as well.