One vector which is obviously perpendicular to [1,0,1] is v=[0,1,0].
A third vector perpendicular to both of them is w=[-1,0,1].
Note: there is a systematic way of finding perpendicular (orthogonal) vectors, but often times trial and error is faster.
Andre W.
tutor
Two vectors are perpendicular when their dot product is zero. So we want a vector [x,y,z] with
[1,0,1]•[x,y,z]=x+z=0.
The simplest choice is x=0=z, and y can be anything except 0. I let y=1 and got v=[0,1,0].
Another simple choice is x=-1, then z=1. Now y has to be zero, or this third vector would not be perpendicular to the second vector, v. That's how I got w=[-1,0,1].
Interestingly, you cannot find a fourth vector which is perpendicular to all three of these.
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10/23/13
Sun K.
10/23/13