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 = )

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- Oct 22nd 2008, 07:34 PMsinni8vector 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 PMJhevon
see example 1 here

Quote:

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

and if you could, why didn't you just ignore the third point and do it? - Oct 22nd 2008, 07:59 PMsinni8
- Oct 22nd 2008, 08:01 PMo_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 PMJhevon