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theneedtoknow
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If I have a vector nhat = [nx, ny, nz] which is normal to some plane, how can I write the vectors (I assume there are infinitely many) which are perpendicular to that plane?
Char. Limit said:Well, normal is perpendicular. So the set of vectors perpendicular to that plane would be any non-zero multiple of [itex]\hat{n}[/itex].
The vector n̂ represents the normal vector to the plane. It is a vector that is perpendicular to every vector in the plane.
To find a vector that is perpendicular to a given plane, you can use the cross product between any two non-parallel vectors in the plane. The resulting vector will be perpendicular to both of the original vectors, and therefore perpendicular to the plane.
Yes, a vector can be perpendicular to an infinite number of planes. This is because there are an infinite number of planes that can contain the vector as its normal vector.
The equation of a plane can be written as Ax + By + Cz = D, where A, B, and C are the components of the normal vector n̂, and D is a constant. This equation represents all points in space that are perpendicular to the vector n̂.
Yes, it is possible for two planes to have the same normal vector. This means that the planes are parallel to each other, and they have the same orientation in space.