h-1.amazonaws.com/pyq-question-images/batch-001/5ba1f030d8fa.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) 2nd April Morning Shift Mathematics - 3D Geometry Question 42 English Explanation">

$$\begin{aligned} & \operatorname{ar}(\triangle A B C)=5 \\ & \frac{1}{2} \times b c=5 \\ & \Rightarrow \quad b c=10 \\ & \operatorname{ar}(\triangle A C D)=6 \\ & \frac{1}{2} \times c d=6 \\ & \Rightarrow \quad c d=12 \\ & \operatorname{ar}(\triangle A B D)=7 \\ & b d=14 \end{aligned}$$

$$\begin{aligned} & \operatorname{area}(\triangle B C D)=\frac{1}{2}|\overrightarrow{B C} \times \overrightarrow{B D}| \\ & \overrightarrow{B C}=<-b, c, 0> \\ & \overrightarrow{B D}=<-b, 0, d> \\ & |\overrightarrow{B C} \times \overrightarrow{B D}|=\sqrt{c^2 d^2+b^2 d^2+b^2 c^2} \\ & =\sqrt{12^2+14^2+10^2} \\ & =\sqrt{440} \\ & \operatorname{ar}(\triangle B C D)=\sqrt{110} \end{aligned}$$

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JEE Main 2025 (Online) 2nd April Morning Shift Mathematics - 3D Geometry Question 42 Hindi Explanation

$$\begin{aligned} & \operatorname{area}(\triangle B C D)=\frac{1}{2}|\overrightarrow{B C} \times \overrightarrow{B D}| \\ & \overrightarrow{B C}=<-b, c, 0&g

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