# Thread: Find two non-parallel unit vectors that are orthogonal to v = <3,-1,2>?

1. ## Find two non-parallel unit vectors that are orthogonal to v = <3,-1,2>?

Find two non-parallel unit vectors that are orthogonal to v = <3,-1,2>?

So far I can only think that

axb = v... then I'm stuck.

2. Originally Posted by s3n4te
Find two non-parallel unit vectors that are orthogonal to v = <3,-1,2>?
Just pick any two that work.

Say $\displaystyle \left\langle {\frac{1} {{\sqrt {10} }},\frac{3} {{\sqrt {10} }},0} \right\rangle \;\& \,\left\langle {0,\frac{2} {{\sqrt 5 }},\frac{1} {{\sqrt 5 }}} \right\rangle$

3. Originally Posted by Plato
Just pick any two that work.

Say $\displaystyle \left\langle {\frac{1} {{\sqrt {10} }},\frac{3} {{\sqrt {10} }},0} \right\rangle \;\& \,\left\langle {0,\frac{2} {{\sqrt 5 }},\frac{1} {{\sqrt 5 }}} \right\rangle$
is there a process in picking them?

4. Originally Posted by s3n4te
is there a process in picking them?
Not really. Just start with vectors that are perpendicular and make them units.
You could have chosen $\displaystyle <1,5,1>~\&~<2,0,-3>$ and made each a unit.

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### find two non-parallel vectors that are both orthogonal to

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