If $a,b,c$ are non negative and distinct numbers and 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 ?

Question

$\begin{array}{1 1} the \;A.M. \;of\; a\:\:and \:\:b \\ the\; G.M. \; of\; a\:\:and \:\:b \\ the\; H.M. \; of \;a\:\:and \:\:b \\ 0 \end{array}$