Question

If the following three linear equations have a non-trivial solution, then
$$\begin{aligned} &x+4 a y+a z=0 \\ &x+3 b y+b z=0 \\ &x+2 c y+c z=0 \end{aligned}$$
(A) $a, b, c$ are in A.P.
(B) $a, b, c$ are in G.P
(C) $a, b, c$ are in H.P.
(D) $a+b+c=0$

Answer 1

Ans: (C)
Hint : To have non-trivial solution, $\left|\begin{array}{lll}1 & 4 a & a \\ 1 & 3 b & b \\ 1 & 2 c & c\end{array}\right|=0 \Rightarrow \frac{1}{c}+\frac{1}{a}=\frac{2}{b}$

Answer 2

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Answer 3

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