Let a, b, c, be distinct and non-negative. If the vectors ai + aj + ck, i + k, and ci + cj + bk lie in a plane, then c is
Answer & explanation
Correct answer: option 2
$\left|\begin{array}{lll}a & a & c \\ 1 & 0 & 1 \\ c & c & b\end{array}\right|=0$
$C_2 \rightarrow C_2-C_1$
$-1\left(a b-c^2\right)=0 \Rightarrow c^2=a b$
Hence (2) is correct answer.