Oct 14, 2017 · When computing the normal vector to a plane with this method of choosing a pair of vectors parallel to the plane, it is necessary that the vectors not be linearly independent.

I am using $3$ D coordinate data from an electromagnetic motion tracker and the reference plane will be constantly moving. I understand the cross product of the two vectors $\vec {AB} \times …

Since we're working in three dimensions, any vector perpendicular to these two displacement vectors will be perpendicular to the plane they determine, and vice versa, so we can use the …

I have a question regarding vectors: Find the equation of the plane perpendicular to the vector $\vec {n}\space= (2,3,6)$ and which goes through the point $ A (1,5,3)$. (A cartesian and …

I'm doing a raytracing exercise. I have a vector representing the normal of a surface at an intersection point, and a vector of the ray to the surface. How can I determine what the …

0 As the OP says, in 3 dimensions you find the plane normal of a plane spanned by two vectors by the cross product. So, the hope is that in N dimensions you can find the normal of a …

I have a triangle represented with three points in $3D$ space and a normal vector of that triangle. How can I determine if the normal vector (starting at $ (0,0,0)$ ) is pointing towards or away fro...

Geometrically speaking, any vector lying on this plane is perpendicular to that normal vector, hence their dot product equaling zero is enough to define a plane. Another way to look at this …

In another question here someone asks why a normal vector of a plane is simply a vector of the coefficients. For example: For the plane $ 2x−y+3z=8 $, a normal vector is $(2,−1,3)$ The …

Since this is true for all vectors in the plane, it’s true for a particular one, so given a normal vector $\mathbf n$ and any element $\mathbf p$ of the plane, you can get a cartesian equation for …