Question 892544
Choose any vector in W. 
Set {{{x=0}}}, then {{{-2y+z=0}}}
{{{2y=z}}}
If {{{y=1}}}, then {{{z=2}}}
(0,1,2)
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Now use the dot product to find a perpendicular vector to this vector.
{{{0*a+1*b+2*c=0}}}
Let {{{a=1}}}
then {{{b=-2c}}}
Let {{{c=1}}}, then {{{b=-2}}}
(1,-2,1)
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Now take the cross product of those two vectors to find a mutually perpendicular vector to these two.
(0,1,2)X(1,-2,1)=(5,2,-1)
So then,
(0,1,2), (1,-2,1), and (5,2,-1) form an orthogonal basis of W.