(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.

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# Orthogonal Vectors in 3-D

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