# Equation of a plane

#### JJ007

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
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 $$\displaystyle (0,1,-1)$$.

#### JJ007

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
$$\displaystyle 17x-y-7z\ =0?$$
Does $$\displaystyle (0,1,-1)$$ belong to that plane?
I think not. So put it in to get the correct constant.