jee-main 2023 Q89

jee-main · India · session1_25jan_shift1 Vectors: Lines & Planes Find Cartesian Equation of a Plane

Let the equation of the plane passing through the line $x - 2 y - z - 5 = 0 = x + y + 3 z - 5$ and parallel to the line $x + y + 2 z - 7 = 0 = 2 x + 3 y + z - 2$ be $a x + b y + c z = 65$. Then the distance of the point $( a , b , c )$ from the plane $2 x + 2 y - z + 16 = 0$ is $\_\_\_\_$.

Let the equation of the plane passing through the line $x - 2 y - z - 5 = 0 = x + y + 3 z - 5$ and parallel to the line $x + y + 2 z - 7 = 0 = 2 x + 3 y + z - 2$ be $a x + b y + c z = 65$. Then the distance of the point $( a , b , c )$ from the plane $2 x + 2 y - z + 16 = 0$ is $\_\_\_\_$.

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