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JEE Main20231 Feb 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let α x + β y + γ z = 1 be the equation of a plane passing through the point 3 , - 2 , 5 and perpendicular to the line joining the points 1 , 2 , 3 and - 2 , 3 , 5 . Then the value of α β y is equal to _____ .

Correct answer

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Step-by-step solution

Given, α x + β y + γ z = 1 be the equation of a plane passing through the point 3 , - 2 , 5 and perpendicular to the line joining the points 1 , 2 , 3 and - 2 , 3 , 5 , Now, normal vector of plane = 1 - - 2 ,   2 - 3 ,   3 - 5 ≡ 3 , - 1 , - 2 So, the equation of Plane will be, 3 x - y - 2 z + λ = 0 Now given, point 3 , - 2 , 5 satisfies the plane 3 × 3 + 2 - 10 + λ = 0 ⇒ λ = - 1 Hence, the equation of plane will be, 3 x - y - 2 z = 1 Now comparing with given

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