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## Homework Statement

Let S, a subspace of ℝ

^{3}be the set of vectors orthogonal to vector (1,2,3)

a)describe Set S

b) find a basis for Set S

**2. Relevant**

__Equations__

That a basis has to be linearly independent and span R^3

## The Attempt at a Solution

[/B]

I would do this:

I know that vector (1,2,3) is the cross product of 2 vectors v1xv2

so I could put it in a matrix (where v1=a,b,c and v2=d,e,f)

a b c

d e f

But I am lost as to describe set S... Wouldn't I need to row reduce to see which variable is free, and then I could say whether or not it is a line or a plane ( well the dimension)