How Do You Find the Equation of a Plane Given a Point and a Perpendicular Line?

[salistoun]

Hi all,

How do you go about solving the following Question?

Find an equation of the plane containing the point (1 , 1 , -1) and perpendicular to the line through the points (2 , 0 , 1) and (1 , -1 , 0).

Stephen

 

[DonAntonio]

Hi all,

How do you go about solving the following Question?

Find an equation of the plane containing the point (1 , 1 , -1) and perpendicular to the line through the points (2 , 0 , 1) and (1 , -1 , 0).

Stephen

Direction vector of the line:

$$\underline v:=(2,0,1)-(1,-1,0)=(1,1,1)$$

So plane perpendicular to the above line is

$$ax+by+cz+d=0\,\,,\,\,with\,\,\,0=(a,b,c)\cdot (1,1,1)=a+b+c=0$$

But this plane also has to contain the point $\,(1,1,-1)\,$ , so it has also to be

$$a+b-c+d=0$$

Now try to continue from here and end the exercise.

DonAntonio

 

[salistoun]

Thanks Don it makes sense.

Stephen