Let the plane meet the co-ordinate axes at the points . If the orthocenter of the triangle is , then is equal to ___.

288 Explanation: Solution: Points nikalna: Plane ki equation: ya . Orthocenter ( ) ki property: Orthocenter hamesha us line par lie karta hai jo origin se plane par perpendicular ho. Plane ka normal vector hai. Isliye origin se orthocenter tak ka vector normal vector ke parallel hoga: Humein diya gaya hai: aur ki value: Final Calculation: Humein nikalna hai: Ans: 288

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let the plane $x + 3y - 2z + 6 = 0$ meet the co-ordinate axes at the points $A, B, C$ . If the orthocenter of the triangle $ABC$ is $(\alpha, \beta, \frac{6}{7})$ , then $98(\alpha + \beta)^2$ is equal to ___.

JEE 2023 — Mathematics PYQ

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