# Equation of a plane

#### Yuuki

##### Member
#q1
how do i find the normal form of a plane given a point thru the plane and a vector parallel to it?

first of all i don't understand what a vector parallel to a plane is :/

#q2

how do i find a unit vector that's orthogonal to a certain vector?

#### Ackbach

##### Indicium Physicus
Staff member
Re: equation of a plane

Q1: Well, what is the normal form for a plane? What does each symbol represent? How could you find an applicable value for each of those symbols from the given data?

Q2: Can you write down an equation that says "vector $\vec{x}$ is orthogonal to vector $\vec{y}$"?

#### Deveno

##### Well-known member
MHB Math Scholar
Re: equation of a plane

You may want to take a look at THIS.

If, after reading that, you still have questions, be more specific and we'll try to help

#### HallsofIvy

##### Well-known member
MHB Math Helper
Re: equation of a plane

#q1
how do i find the normal form of a plane given a point thru the plane and a vector parallel to it?
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.

first of all i don't understand what a vector parallel to a plane is :/
Well, since a vector is "movable" this is the same a vector lying in the plane.

#q2

how do i find a unit vector that's orthogonal to a certain vector?
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.

#### Ackbach

##### Indicium Physicus
Staff member
Re: equation of a plane

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.
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.