Let $a,b$ and $c$ be distinct non-negative numbers. If the vectors $a\hat{i}+a\hat{j}+c\hat{k}$, $\hat{i}+\hat{k}$ and $c\hat{i}+c\hat{j}+b\hat{k}$ lie in a plane, then $c$ is:

1. A
   the Geometric Mean of $a$ and $b$
2. B
   the Arithmetic Mean of $a$ and $b$
3. C
   equal to zero
4. D
   the Harmonic Mean of $a$ and $b$