Let the equation of plane passing through the line of intersection of the planes \(x+2 y+a z=2\) and \(x-y+z=3\) be \(5 x-11 y+b z=6 a-1\). For \(c \in Z\), if the distance of this plane from the point \((a,-c, c)\) is \(\frac{2}{\sqrt{a}}\), then \(\frac{a+b}{c}\) is equal

[JEE Main 2023, 13 Apr (Shift 1)]

Question

Let the equation of plane passing through the line of intersection of the planes \(x+2 y+a z=2\) and \(x-y+z=3\) be \(5 x-11 y+b z=6 a-1\). For \(c \in Z\), if the distance of this plane from the point \((a,-c, c)\) is \(\frac{2}{\sqrt{a}}\), then \(\frac{a+b}{c}\) is equal

[JEE Main 2023, 13 Apr (Shift 1)]

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Let the equation of plane passing through the line of intersection of the planes \(x+2 y+a z=2\) and \(x-y+z=3\) be \(5 …

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