jee-main 2020 Q61

jee-main · India · session1_09jan_shift1 Vectors: Lines & Planes Coplanarity and Relative Position of Planes

If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three planes $x + 4 y - 2 z = 1$ $x + 7 y - 5 z = \beta$ $x + 5 y + \alpha z = 5$ is a line in $R ^ { 3 }$, then $\alpha + \beta$ is equal to:
(1) 0
(2) 10
(3) 2
(4) - 10

If for some $\alpha$ and $\beta$ in $R$, the intersection of the following three planes\\
$x + 4 y - 2 z = 1$\\
$x + 7 y - 5 z = \beta$\\
$x + 5 y + \alpha z = 5$\\
is a line in $R ^ { 3 }$, then $\alpha + \beta$ is equal to:\\
(1) 0\\
(2) 10\\
(3) 2\\
(4) - 10

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