Solution: Since $C$ divides $AB$ in the ratio $2:3$, the position vector of $C$ is given by the section formula:

Wed, 06 May 2026 14:36:39 +0000

**1. Intro: The Hidden Math Shaping Digital Conversations** Ever scanned a math formula and wondered how it explains real-life relationships? In data, design, and even social trends, ratios like 2:3 pop up as powerful tools for understanding division, balance, and positioning—concepts increasingly relevant in digital spaces. Today, we explore how dividing a line segment in a 2:3 ratio using vector geometry isn’t just abstract math—it’s quietly influencing how we interpret balance in everything from online engagement to income sharing. For curious U.S.-based readers navigating data-driven decisions, understanding this simple ratio can unlock clearer thinking about trends, fairness, and allocation in a complex digital world. --- **2. Why This Ratio Matters in the US Digital Landscape**