JEE Main: Shortest Distance Given → Find α Smartly 💡
❓ Concept 🎬 Shortest Distance in 3D (α-based) in 59 Sec JEE 3D geometry mein jab shortest distance diya ho aur α parameter direction ratios mein aa jaaye — samajh lo cross product ka real test start ho gaya hai 🔥 🖼️ Concept Image ✍️ Short Explanation Shortest distance problems formula-based hote hain, lekin jab parameter (α) involve ho, toh goal hota hai: 👉 SD ko α ke function mein convert karna 👉 Given distance se equation banana 👉 α ke possible values nikaalna (ya unka sum) 🔹 Step 1 — Lines in Symmetric Form Agar line di ho: x − x 1 a 1 = y − y 1 b 1 = z − z 1 c 1 Toh: Direction vector d ⃗ 1 = ( a 1 , b 1 , c 1 ) \vec d_1=(a_1,b_1,c_1) Point on line A ( x 1 , y 1 , z 1 ) A(x_1,y_1,z_1) Similarly, second line ke liye: d ⃗ 2 = ( a 2 , b 2 , c 2 ) \vec d_2=(a_2,b_2,c_2) and point B ( x 2 , y 2 , z 2 ) B(x_2,y_2,z_2) . 📌 Agar α direction ratios mein hai, toh d ⃗ 2 \vec d_2 α pe depend karega . 🔹 Step 2 — Shortest Distance Formula (...