Answer
$(11,1,22)$
Work Step by Step
$\vec{a}+2 (\vec{b}+\vec{c})=(5,1,0)+2[(2,-1,9) +(1,1,2) \\=(5,1,0)+2[(2+1,-1+1,9+2) \\=(5,1,0)+2(3,0,11)\\=(5,1,0)+(6,0,22)\\=(5+6, 1+0, 0+22) \\=(11,1,22)$
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