JEE Advance - Mathematics (1993 - No. 1)
Let $$a, b, c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is
the Arithmetic Mean of $$a$$ and $$b$$
the Geometric Mean of $$a$$ and $$b$$
the Harmonic Mean of $$a$$ and $$b$$
equal to zero