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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 :

( A ) the geometric mean of a and b
( B ) the arithmetic mean of a and b
( C ) equal to zero
( D ) the harmonic mean of a and b

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