# Linear Algebra(parametric equations)

The question states:
Determine the parametric equations of the line passing through the point P(2,1,0) and perpendicular to the plane 2x-5y=6.

The equation to obviously use is the "point-parallel" I'm guessing. X= P +tV where P is the point and V is a vector, and X=(x,y,z). But how would I use this since there isn't a vector given for V and instead is the plane 2x-5y=6? Maybe this isn't the one I need to use. Please help.

Dick
Homework Helper
The direction vector for the line is the normal to the plane. Do you know how to find the normal to a plane?

The direction vector for the line is the normal to the plane. Do you know how to find the normal to a plane?

n . (x - p) ?

Dick
Homework Helper
You can also write that as n.(x,y,z)=constant. What's a normal for your plane?

You can also write that as n.(x,y,z)=constant. What's a normal for your plane?

hm I honestly have no idea how to do this problem. I could set it up like this but then what would I do next?

N . (( x,y,z) - (2,1,0)= 0

x-2
y-1
z-0 ????

Dick
Homework Helper
You don't need the point P to find the normal to the plane. Please look up how to find the normal to a plane ax+by+cz=constant.

You don't need the point P to find the normal to the plane. Please look up how to find the normal to a plane ax+by+cz=constant.

Ok im not really finding too much on the topic.. I did however find one thing that said you want to use the cross product to find the norm to the plane.

would the norm happen to be (0,0,-4)

Dick
Homework Helper
No, one choice for the normal would be (2,-5,0). Now where did I get that?

No, one choice for the normal would be (2,-5,0). Now where did I get that?

ahhh from the equation itself. so that would be the case everytime?

ahhh from the equation itself. so that would be the case everytime?

Whenever looking at the equation of a plane in the form ax + by + cz + d = 0, the vector (a,b,c) is always the vector that is perpendicular to the plane (which is a normal vector). Since you are trying to find the direction vector for a line perpendicular to the given plane, finding the direction vector is easy. You also have the point P, so you should be able to answer it now.

Dick