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If for some \(\alpha\) and \(\beta\) in \(R\), the intersection of the following three planes \[\begin{aligned}& x+4 y-2…

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If for some \(\alpha\) and \(\beta\) in \(R\), the intersection of the following three planes
\[\begin{aligned}& x+4 y-2 z=1 \\& x+7 y-5 z=\beta \\& x+5 y+\alpha z=5\end{aligned}\] is a line in \(R ^3\), then \(\alpha+\beta\) is equal to :


[JEE Main 2020, 9 Jan (Shift 1)]

a

10

b

\( -10 \)

c

2

d

0

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