Let , and . Find a vector such that and .
q - r = 3
2r - p = -8
p - 2q = 2
(Do you see where these equations come from?)
These equations are not all independent. You can't solve for p, q and r yet. But you also know that d.a = 0. So you also have:
p + q - 2r = 0
Now you can solve for p, q and r.