A) geometric mean of a and b
B) arithmetic mean of a and b
C) zero
D) harmonic mean of a and b
Correct Answer: A
Solution :
Given, points lie in a plane, if \[\left| \begin{matrix} a & a & c \\ 1 & 0 & 1 \\ c & c & b \\ \end{matrix} \right|=0\] Applying \[{{C}_{1}}\to {{C}_{1}}-{{C}_{2}}\] \[\Rightarrow \] \[\left| \begin{matrix} 0 & a & c \\ 1 & 0 & 1 \\ 0 & c & b \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[-1[ab-{{c}^{2}}]=0\] \[\Rightarrow \] \[{{c}^{2}}=ab\] Hence, c is the geometric mean of o and b.
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