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How do I find an orthonormal basis for a plane defined as $x_1+x_2+x_3=0$? I don't know where to start -- not even given dimensions. Thank you.

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    Do you mean a plane in $\mathbb{R}^3$ given as $ax+by+cz=0$?2011-03-04
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    In general: find an arbitrary basis, and apply Gram-Schmidt.2011-03-04
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    @Arturo: I am not given dimensions, which is part of my confusion.2011-03-04
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    What does "a+b+c=0" mean, then? Are a, b, and c constants? Variables? Do you know the dimension of the ambient space?2011-03-04
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    @Arturo: a, b, and c are variables (it was given by x_1 x_2 and x_3 in the textbook). Nothing stated about the dimensions.2011-03-04
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    @John: You should stick to $x_1$, $x_2$, and $x_3$. Those are *clearly* variables, whereas $a$, $b$, and $c$ are usually constants or scalars.2011-03-04

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