Doubtify – JEE Ki Taiyaari, Simple Bhasha Mein

  ❓ Concept 🎬 3D Line Through a Point & Two Lines JEE 3D geometry mein ek super-common pattern hota hai: 👉 A line L passes through a fixed point and intersects two given lines. Iska matlab hai — L ko define karne ke liye bas parameter aur collinearity ka game khelo. ✍️ Short Explanation Trick simple hai: ✔ Dono lines ki parametric form likho ✔ Assume intersection points ✔ Use collinearity with the fixed point ✔ Solve parameters ✔ Get direction of L → equation ready! 🔹 Step 1 — Write Given Lines in Parametric Form Suppose: r ⃗ = a ⃗ 1 + λ d ⃗ 1 \vec r = \vec a_1 + \lambda \vec d_1 r ⃗ = a ⃗ 2 + μ d ⃗ 2 \vec r = \vec a_2 + \mu \vec d_2 Where a ⃗ 1 ,   a ⃗ 2 \vec a_1,\ \vec a_2  = position vectors of known points d ⃗ 1 ,   d ⃗ 2 \vec d_1,\ \vec d_2 ​ = direction vectors 🔹 Step 2 — Find Intersection Points with L Assume the line L passes through a fixed point P P P . Let A = a ⃗ 1 + λ d ⃗ 1 A = \vec a_1 + \lambda \vec d_1 B = ...