Vectors Made Easy! 🎯 Find Modulus Using External Division & Ratio Theorem

📌 In this video, we explore *Vectors**, focusing on how to find the **length (modulus) of a vector* using the *Ratio Theorem* and external division. 🧮 Problem Breakdown: Points *P* and *Q* are such that: OP = i + 2j + 3k OQ = 4i + 5j – 3k A point *M* divides *PQ externally in the ratio 3:2* 🎯 Task: Find the **modulus of vector MQ**, given that **O is the origin**. ✅ What You'll Learn: How to interpret external division of vectors Using the Ratio Theorem correctly for external points Finding position vectors and computing differences Calculating the modulus (length) of a 3D vector Step-by-step breakdown of vector subtraction and modulus formula ⏱️ TIMESTAMPS: 0:00 - Introduction 0:27 - Understanding the given ratio and external division 1:30 - Using the Ratio Theorem to find OM 3:45 - Finding vector MQ using subtraction 6:45 - Computing modulus of MQ 8:15 - Final Answer 👩‍🏫 Perfect for: KCSE and IGCSE candidates Form 3/4 high school students Math teachers explaining 3D vectors Anyone learning vector geometry 🔔 Don't forget to: ✔️ Like the video ✔️ Subscribe for more math tutorials ✔️ Comment below if you'd like more examples like this 📢 Share this video with your classmates! #Vectors #RatioTheorem #KCSEMath #IGCSEVectors #3DGeometry