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JEE Main202126 Feb 2021Morning ShiftMathematicsThree Dimensional GeometryActual

Let λ , 2 , 1 be a point on the plane which passes through the point 4 , - 2 , 2 . If the plane is perpendicular to the line joining the points - 2 , - 21 , 29 and - 1 , - 16 , 23 , then λ 11 2 - 4 λ 11 - 4 is equal to ________.

Correct answer

0

Step-by-step solution

A B → . P Q → = 0 ⇒ i ^ + 5 j ^ - 6 k ^ . 4 - λ i ^ - 4 j ^ + k ^ = 0 ⇒ 4 - λ - 20 - 6 = 0 ⇒ λ = - 22 ⇒ λ 11 2 - 4 λ 11 - 4 = 4 + 8 - 4 = 8

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