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:

• A
  the arithmetic mean of $a$ and $b$.
• B
  the harmonic mean of $a$ and $b$.
• C
  the geometric mean of $a$ and $b$.
• D
  not the arithmetic mean of $a$ and $b$.