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