(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The problem is more of a concept/visual problem, like to find out if it's true or false and why:

all vectors orthogonal to a non zero vector in R^3 are contained in a straight line.

2. Relevant equations

No equations, just very bad at visualizing in 3-D

3. The attempt at a solution

I know that for a vector to be orthogonal, it needs to be at 90 degrees with another (non zero vector). So, when I visualize it in my head, I see a straight line ( a vector) going out in the middle of a 3-D cube from the middle. Then, if I take a 90 degrees anywhere along the line, I see a "normal" 90 degree line, but I can rotate that normal line all around that point, so I think I should always get a plane and not a line, but I'm not sure if all vectors are like that because I don't know if a vector in R^3 can be a line like that. Or, if I had a plane and then a "normal" plane going at it at 90 degrees, then all of those "normals" also form a plane. So, I think that it's true that ALL vectors orthogonal to a non zero vector in R^3 are contained in a straight line.

I'm in my first year at college in Matrix Theory/Linear algebra.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Orthogonal Vectors in 3-D

**Physics Forums | Science Articles, Homework Help, Discussion**