JEE Main: Unit Vectors + Dot–Cross Product Made Easy 💡
❓ Concept 🎬 Dot–Cross Product Combo Trick in 59 Sec JEE vectors mein jab dot product aur cross product ek saath dikh jaaye, toh students confuse ho jaate hain. Reality? 👉 Poora game orthogonality ka hota hai. Agar perpendicularity samajh aa gayi, toh calculation automatic zero ban jaati hai 🔥 🖼️ Concept Image ✍️ Short Explanation Vector questions mein sabse common trap hota hai: ❌ Cross product ko unnecessarily expand karna Jabki JEE ka smart rule hai: 👉 Dot product + cross product = perpendicularity check 🔹 Step 1 — Unit Vectors Basics Agar â aur b̂ unit vectors hain: a ^ ⋅ a ^ = 1 \hat a\cdot\hat a=1 b ^ ⋅ b ^ = 1 \hat b\cdot\hat b=1 a ^ ⋅ b ^ = cos θ \hat a\cdot\hat b=\cos\theta 📌 Unit vector ka magnitude 1 hota hai — always. 🔹 Step 2 — Cross Product Direction (KEY IDEA 🔥)** a ^ × b ^ \hat a\times\hat b 👉 â aur b̂ dono ke perpendicular hota hai. Isliye: ( a ^ × b ^ ) ⋅ a ^ = 0 (\hat a\times\hat b)\cdot\hat a=0 ( a ^ × b ^ ) ⋅ b ^ = 0 (...