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JEE Main20204 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

If the equation of a plane P , passing through the intersection of the planes, x + 4 y - z + 7 = 0 and 3 x + y + 5 z = 8 is a x + b y + 6 z = 15 for some a , b ∈ R , then the distance of the point 3 , 2 , - 1 from the plane P is … …

Correct answer

3

Step-by-step solution

Equation of plane of passing through intersection of planes P 1 ⇒ x + 4 y − z + 7 = 0 ...... 1 and P 2 ⇒ 3 x + y + 5 z − 8 = 0 ..... 2 is P 1 + λ P 2 = 0 x + 4 y − z + 7 + λ 3 x + y + 5 z − 8 = 0 3 λ + 1 x + λ + 4 y + 5 λ − 1 z + 7 − 8 λ = 0 ....... 3 a x + b y + 6 z − 15 = 0 ........ 4 On comparing 3 and 4 , a 3 λ + 1 = b λ + 4 = 6 5 λ − 1 = − 15 7 − 8 λ ∴ 42 − 48 λ = − 7

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