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JEE Main202118 Mar 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Let the mirror image of the point ( 1 , 3 , a ) with respect to the plane r → · ( 2 i ^ - j ^ + k ^ ) - b = 0 be ( - 3 , 5 , 2 ) . Then the value of a + b is equal to ___ .

Correct answer

0

Step-by-step solution

plane = 2 x - y + z = b Mid-point R ≡ - 1 , 4 , a + 2 2 → lies on plane ∴ - 2 - 4 + a + 2 2 = b ⇒ a + 2 = 2 b + 12 ⇒ a = 2 b + 10 Direction ratios of P Q → = 4 , - 2 ,   a - 2 P Q → is parallel to the normal vector of plane. ∴ 2 4 = - 1 - 2 = 1 a - 2 ⇒ a - 2 = 2 ⇒ a = 4 , b = - 3 ∴ | a + b | = 1

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