# vector equation of plane

• Oct 22nd 2008, 07:34 PM
sinni8
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 = )
• Oct 22nd 2008, 07:44 PM
Jhevon
Quote:

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

Quote:

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?
• Oct 22nd 2008, 07:59 PM
sinni8
Quote:

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!!
• Oct 22nd 2008, 08:01 PM
o_O
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: $\displaystyle a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$
• Oct 22nd 2008, 08:11 PM
Jhevon
Quote:

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.