A) the GM of a and b
B) the AM of a and b
C) the HM of a and b
D) equal to zero
E) None of the above
Correct Answer: A
Solution :
Since, vectors\[a\hat{i}+a\hat{j}+c\hat{k},\hat{i}+\hat{k}\]and\[c\hat{i}+c\hat{j}+b\hat{k}\] are coplanar, therefore \[\left| \begin{matrix} a & a & c \\ 1 & 0 & 1 \\ c & c & b \\ \end{matrix} \right|=0\] \[\Rightarrow \] \[{{c}^{2}}=ab\] \[\Rightarrow \] c is the GM of a and b.
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