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 = )
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: $\displaystyle a(x-x_0) + b(y-y_0) + c(z-z_0) = 0$