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Introduction to Vectors: Components and Magnitude | Calculus III

In this video, we introduce vectors, one of the foundational ideas in Calculus III. You’ll learn what vectors are, why they matter, and how to work with their components and magnitude.

We focus on conceptual understanding first—what vectors represent geometrically and physically—before moving on to computations in later lessons.

In this video, you will learn:
• Why vectors are essential in multivariable calculus
• How vectors model real-world quantities like velocity, force, and direction
• What vector components represent geometrically
• How to compute the magnitude of a vector using the Pythagorean Theorem
• Why magnitude matters for comparing vectors and building unit vectors

This lesson sets the stage for everything that follows in Calculus III, including vector operations, motion in space, and vector-valued functions.

What’s next:
• Unit vectors and direction
• Vector addition and scalar multiplication
• Vectors in three dimensions