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JEE Main202131 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Suppose the line x - 2 α = y - 2 - 5 = z + 2 2 lies on the plane x + 3 y - 2 z + β = 0 . Then ( α + β ) is equal to .

Correct answer

0

Step-by-step solution

Given the line x - 2 α = y - 2 - 5 = z + 2 2 2 ,   2 ,   - 2 Lies in plane Equation of plane x + 3 y - 2 z + β = 0 2 + 3 × 2 - 2 × - 2 + β = 0 2 + 6 + 4 + β = 0 β = - 12 The direction ratio of the line are α , - 5 , 2 The line is in the plane α × ( 1 ) - 5 × ( 3 ) + 2 × ( - 2 ) = 0   α = 19 Hence, α + β = 19 - 12 = 7

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