a = i - j, b = j - k, c = k - i: unit vector d with a.d = 0 and b, c, d coplanar

1. A.
   $\pm\frac{1}{\sqrt{3}}(1,1,1)$
2. B.
   $\pm\frac{1}{\sqrt{3}}(-1,-1,1)$
3. C.
   $\pm\frac{1}{\sqrt{6}}(1,1,-2)$
4. D.
   $\pm\frac{1}{\sqrt{2}}(1,1,0)$

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1. A.
   $\pm \left( \frac{\widehat{i} + \widehat{j} + 3\widehat{k}}{\sqrt{11}} \right)$
2. B.
   $\pm \left( \frac{- \widehat{j} + \widehat{k}}{\sqrt{2}} \right)$
3. C.
   $\pm \left( \frac{\widehat{i} + \widehat{j} + \widehat{k}}{\sqrt{3}} \right)$
4. D.
   $\pm \left( \frac{\widehat{i} + \widehat{j} - 2\widehat{k}}{\sqrt{6}} \right)$

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