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If the system of linear equations \(\begin{aligned}& 2 x+2 a y+a z=0 \\& 2 x+3 b y+b z=0 \\& 2 x+4 c y+c z=0\end{aligned…

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If the system of linear equations
\(\begin{aligned}& 2 x+2 a y+a z=0 \\& 2 x+3 b y+b z=0 \\& 2 x+4 c y+c z=0\end{aligned}\)

where \(a, b, c \in R\) are non-zero and distinct; has a non-zero solution, then

[JEE Main 2020, 7 Jan (Shift 1)]

a

\(a, b, c\) are in A.P.

b

\(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in A.P.

c

\(a+b+c=0\)

d

\(a, b, c\) are in G.P.

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