JEE-Advanced 2015 (11/40)

Geometry Level 3

In \(\mathbb{R}^3\), consider the planes \(P_1:y=0\) and \(P_2:x+z=1\). Let \(P_3\) be a plane, different from \(P_1\) and \(P_2\), which passes through the intersection of \(P_1\) and \(P_2\). If the distance of the point \((0,1,0)\) from \(P_3\) is \(1\) and the distance of a point \((\alpha,\beta,\gamma)\) from \(P_3\) is \(2\), then which of the following relations is(are) true ? \[\begin{array}{} (1) \, 2\alpha+\beta+2\gamma+2=0 \quad \quad \quad \quad & (2) \, 2\alpha-\beta+2\gamma+4=0 \\ (3) \, 2\alpha+\beta-2\gamma-10=0 & (4) \, 2\alpha-\beta+2\gamma-8=0 \end{array}\]
Note :

  • Submit your answer as the increasing order of the serial numbers of all the correct options.

  • For eg, if your answer is \((1),(2)\), then submit \(12\) as the correct answer, if your answer is \((2),(3),(4)\), then submit \(234\) as the correct answer.

×

Problem Loading...

Note Loading...

Set Loading...