You can't. A vector parallel to a plane defines a line (through the given point) in the plane. But there are an infinite number of planes containing a given line.#q1
how do i find the normal form of a plane given a point thru the plane and a vector parallel to it?
Well, since a vector is "movable" this is the same a vector lying in the plane.first of all i don't understand what a vector parallel to a plane is :/
There are an infinite number of vectors orthogonal to a given vector. One way find one of them is to find the equation of the plane containing (0, 0, 0) perpendicular to the given vector. Choose any point in that plane and construct the vector from (0, 0, 0) that point. Finally, calculate the length of that vector and divide the vector by its length to get a unit vector.#q2
how do i find a unit vector that's orthogonal to a certain vector?
Right, I thought of that. But it may be that the OP is actually given a vector that defines a line (there's another point on the line). A line and a point not on the line will uniquely determine a plane, at least in Euclidean geometry.You can't. A vector parallel to a plane defines a line (through the given point) in the plane. But there are an infinite number of planes containing a given line.