Equation of a plane

Nov 2009
38
0
Write an equation of the plane that contains the line \(\displaystyle \frac{x}{1}=\frac{y-1}{3}=\frac{z+1}{2}\) and is perpendicular to the line \(\displaystyle \frac{x-1}{-17}=\frac{y+5}{1}=\frac{z-3}{7}\)

I know how to find the equation for EACH line but how do you do it for the whole plane?

Thanks
 

Plato

MHF Helper
Aug 2006
22,461
8,633
Write an equation of the plane that contains the line \(\displaystyle \frac{x}{1}=\frac{y-1}{3}=\frac{z+1}{2}\) and is perpendicular to the line \(\displaystyle \frac{x-1}{-17}=\frac{y+5}{1}=\frac{z-3}{7}\)
Because it is perpendicular the normal is \(\displaystyle <-17,1,7>\).
We want it to contain the line use the point \(\displaystyle (0,1,-1)\).
 
Nov 2009
38
0
Because it is perpendicular the normal is \(\displaystyle <-17,1,7>\).
We want it to contain the line use the point \(\displaystyle (0,1,-1)\).
\(\displaystyle 17x-y-7z\ =0?\)
 

Plato

MHF Helper
Aug 2006
22,461
8,633
\(\displaystyle 17x-y-7z\ =0?\)
Does \(\displaystyle (0,1,-1)\) belong to that plane?
I think not. So put it in to get the correct constant.