  We prove that the existence of best coapproximation to any element of the
normed linear space out of any one dimensional subspace and its coincidence
with the best approximation to that element out of that subspace characterizes
a real inner product space of dimension $ > 2 $. We conjecture that a finite
dimensional real smooth normed space of dimension $ >2 $ is an inner product
space iff given any element on the unit sphere there exists a strongly
orthonormal Hamel basis in the sense of Birkhoff-James containing that element.
This is substantiated by our result on the spaces $(R^n,\|.\|_p).$
