Q: Show that the vectors a=(1,2,1); b=(0,0,1) and c=(2,-1,1) for a non-orthogonal basis (I guess I can just show that a.b, a.c and b.c all doesn't equal 0?). Using the scalar triple product, write the vector d=(1,1,1) in terms of this basis.

I have been able to find the reciprocal vectors for a, b and c:

$\displaystyle

\begin{array}{l}

a' = \frac{1}{5}(i + 2j) \\

b' = \frac{1}{5}( - 3i - j + 5k) \\

c' = \frac{1}{5}(2i - j) \\

\end{array}

$

but now I don't know what to do to re-write d in terms of the original 2 basis a, b, c. Help would be greatly appreciated.