If the equation of the plane that contains the point and is perpendicular to each of the planes and is , then

15 Explanation: 1. Normal Vectors ko pehchanna: Diye gaye do planes ke normal vectors (coefficients of ) niche diye gaye hain: 2. Naye plane ka Normal Vector ( ) nikalna: Kyunki hamara plane dono planes ke perpendicular hai, iska normal dono aur ka cross product hoga: Determinant solve karne par: 3. Plane ki Equation banana: Plane point se guzarta hai aur uska normal vector hai. Equation ka formula: 4. Compare karna aur Final Answer: Question mein di gayi equation se compare karne par: Ab humein ka maan nikalna hai:

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

If the equation of the plane that contains the point $(-2, 3, 5)$ and is perpendicular to each of the planes $2x + 4y + 5z = 8$ and $3x - 2y + 3z = 5$ is $\alpha x + \beta y + \gamma z + 97 = 0$ , then $\alpha + \beta + \gamma = ?$

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