Question

Let a, b, c be distinct non-negative numbers. If the vectors $ai+aj+ck+,i+k$ and $ci+cj+bk$ lie in a plane, then c is

• A. the $A\cdot M\cdot$ of a and b
• B. the $G\cdot M\cdot$ of a and b
• C. the $H\cdot M\cdot$ of a and b
• D. equal to zero

Answer 1

Answer: (B)

the $G\cdot M\cdot$ of a and b

$ai+aj+ck+,i+k$ and $ci+cj+bk$ are coplanar.
$\Rightarrow \left|\begin{array}{ccc}a& a& c\\ 1& 0& 1\\ c& c& b\end{array}\right|=0$
$\Rightarrow -ac-ab+ac+c^2=0$
$\Rightarrow c^2=ab$
i.e $c$ is GM of $a$ and $b$
Hence, option B.