Let $a, b, c$ 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:
- Athe arithmetic mean of $a$ and $b$.
- Bthe harmonic mean of $a$ and $b$.
- Cthe geometric mean of $a$ and $b$.
- Dnot the arithmetic mean of $a$ and $b$.
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