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JEE Main202127 Jul 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let a plane P pass through the point 3 , 7 , - 7 and contain the line, x - 2 - 3 = y - 3 2 = z + 2 1 . If distance of the plane P from the origin is d , then d 2 is equal to

Correct answer

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Step-by-step solution

The required plane passes through the point 3 , 7 , - 7 . Assume, the equation of the plane is a x - 3 + b y - 7 + c z + 7 = 0 The line x - 2 - 3 = y - 3 2 = z + 2 1 lies on the required plane. So, we can say that a 2 - 3 + b 3 - 7 + c - 2 + 7 = 0 ⇒ - a - 4 b + 5 c = 0           . . . 1 And - 3 × a + 2 × b + 1 × c = 0           . . . 2 Use cross-multiplication to solve the equations 1   &   2 a - 4 × 1 - 2 × 5 = b 5 &#215

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