You get to choose any two non-zero vectors $v ∈ \mathbb{R}^3$ and $u∈\mathbb{R}^3$. How can I find an equation for a plane?

Question

How do I find the equation of the plane or the line that is spanned by the vectors $u$ and $v$.

I just don't understand what the question means when they ask me to find the equation.

score 1 · Answer 1 · answered Dec 22 '14 at 16:38

1

Do you know what the equation of a plane is? To find the Cartesian equation of a plane, you need a point on the plane and a normal vector. If you are given two vectors in the plane, you can take their cross product to find a normal vector. Then you choose any point on any of the vectors in the plane as your point in the plane, and you can easily find the Cartesian equation.

answered Dec 22 '14 at 16:38

user141592

6,206

http://en.wikipedia.org/wiki/Plane_%28geometry%29#Point-normal_form_and_general_form_of_the_equation_of_a_plane – user141592 Dec 22 '14 at 16:39

score 0 · Answer 2 · answered Dec 22 '14 at 16:59

0

Hint #1: the vectors of this plane are exactly the same vectors, who are perpendicular to $u\times v$.

answered Dec 22 '14 at 16:59

peterh

2,756

score 0 · Answer 3 · answered Dec 22 '14 at 17:21

0

If you have $u\times v=(a,b,c)$ then the points $(x,y,z)$ in the plane will satisfy $$ax+by+cz=0.$$ That's because $(x,y,z)$ must be perpendicular to the direction $u\times v$.

answered Dec 22 '14 at 17:21

janmarqz

10,891

You get to choose any two non-zero vectors $v ∈ \mathbb{R}^3$ and $u∈\mathbb{R}^3$. How can I find an equation for a plane?

3 Answers3