Are There Infinite Plane Formulas for a Given Vector?

[skiboka33]

While working through a problem I arrived at a stage where a vector, say V being parallel to the plane I'm trying to find the formula for. Taking the normal vector of the plane to be n I used the dot product:

n*V=0

in this case I knew V to be <-2, -2, -1> and n I set to <a,b,c>. This leads to the equation -2a - 2b - c = 0 for which there are infinite solutions. Does this mean that a plane has an infinite number of equations of have I done somethign wrong?

 

[hypermorphism]

(a,b,c) are the components of a vector normal to V. Thus you have found the equation whose points are endpoints of vectors normal to V. If you are looking for the plane that contains V, this isn't it.
Given a vector in a plane, you need at least one other non-collinear vector in the plane to find the equation of the plane.

 

[skiboka33]

I'm looking for the place parallel to V and I have one point on the plane.

 

[rachmaninoff]

Your plane as an infinite number of points in it (vectors which are solutions to your equation). The are all solutions of one equation:

-2a - 2b - c = 0

 

[hypermorphism]

I'm looking for the place parallel to V and I have one point on the plane.

You will need at least one more point on the plane, so that you can have two noncollinear vectors that lie in the plane. A space parallel with one vector only describes a line.

 

[skiboka33]

You will need at least one more point on the plane, so that you can have two noncollinear vectors that lie in the plane. A space parallel with one vector only describes a line.

True enough. I am actually given 2 points on the plane, sorry.

So i found a vector PQ on the plane (where P and Q are points on the plane). and a Vector V which is parallel to that. Now I'm stuck again

 

[hypermorphism]

Is the vector V collinear with PQ ? Is the plane supposed to pass through the origin ?
If all you want is a plane that contains lines parallel to the vector V, you have an infinitude of planes to choose from.

 

[skiboka33]

That was my first guess too, but since this is an assignment question I'm assuming that's not the case, so I must be missing something... As far as I can see, for a given vector there are an infinite number of planes that could be parallel to it. Even the concept of vectors being parallel to planes doesn't seem to make sense to me.