batch-001/11b89c4112a7.webp" data-orsrc="https://uploads-pracbee-ramanuj.s3.ap-south-1.amazonaws.com/pyq-question-images/batch-001/11b89c4112a7.webp" loading="lazy" style="max-width:100%;height:auto;display:block;margin:0 auto;max-height:40vh;vertical-align:baseline" alt="JEE Main 2025 (Online) 3rd April Morning Shift Mathematics - 3D Geometry Question 37 English Explanation">

$$\begin{aligned} & A=(\alpha, \beta, 4)=(2 \lambda+1,3 \lambda+2,4 \lambda+3) \\ & \text { and } B=(a, b, c)=(\mu+6, \mu,-\mu+4) \\ & \because \frac{\mu+2}{2 \lambda-3}=\frac{\mu-1}{3 \lambda+1}=\frac{-\mu+4}{4 \lambda+3} \\ & \therefore \quad \lambda \mu+8 \lambda+4 \mu=1 \quad \ldots(1)\\ & \text { and } 7 \lambda \mu-16 \lambda+4 \mu=7 \quad \ldots(2) \end{aligned}$$

from equation (1) and (2)

$$\lambda=-1 \text { and } \mu=3$$

Or $\lambda=-\frac{1}{3}$ and $\mu=1$

By taking, $\lambda=-1$ and $\mu=3$, we get

$$\begin{aligned} & \therefore \quad A(\alpha, \beta, 4)=(-1,-1,-1) \\ & \text { and } B(a, b, c)=(9,3,1) \end{aligned}$$

$$\therefore\left|\begin{array}{ccc} 1 & 0 & 1 \\ -1 & -1 & -1 \\ 9 & 3 & 1 \end{array}\right|=8$$

19:T590,

JEE Main 2025 (Online) 3rd April Morning Shift Mathematics - 3D Geometry Question 37 Hindi Explanation

$$\begin{aligned} & A=(\alpha, \beta, 4)=(2 \lambda+1,3 \lambda+2,4 \lambda+3) \\ & \text { तथा } B=(a, b, c)=(\mu+6, \mu,-\mu+4) \\ & \because \frac{\mu+2}{2 \lambda-3}=\frac{\mu-1}{3 \lambda+1}=\frac{-\mu+4}{4 \lambda+3} \\ & \therefore \quad \lambda \mu+8 \lambda+4 \mu=1 \quad \ldots(1)\\ & \text { तथा

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