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)]

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

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