Let be the set of all for which the vectors , and , where , are coplanar, then is equal to:

2290 Explanation: Step 1: Coplanarity ki condition Teen vectors tab coplanar hote hain jab unka Scalar Triple Product zero ho. Iska matlab unke coefficients se bana determinant zero hona chahiye: Step 2: Determinant ko solve karna Step 3: Di gayi equation ka upyog Humein sawal mein diya gaya hai ki , yani . Is value ko equation (i) mein rakhte hain: Step 4: Quadratic equation solve karna Ab hum ke factors nikalenge: Yahan se ki do values aati hain: Toh set . Step 5: Final calculation Humein nikalna hai: Pehla pair : Doosra pair : Kul yog (Total sum): Sahi Uttar: (3) 2290

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JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $S$ be the set of all $(\lambda, \mu)$ for which the vectors $\lambda \hat{i} - \hat{j} + \hat{k}$ , $\hat{i} + 2\hat{j} + \mu \hat{k}$ and $3\hat{i} - 4\hat{j} + 5\hat{k}$ , where $\lambda - \mu = 5$ , are coplanar, then $\sum_{(\lambda, \mu) \in S} 80(\lambda^2 + \mu^2)$ is equal to:

JEE 2023 — Mathematics PYQ

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