Скачать или смотреть The Dot Product — Multivariable Calculus

In this video, we explore the dot product – not just as a formula, but as a way to understand how two vectors relate to each other.

Instead of focusing on computation, we build intuition for what the dot product measures geometrically, and why it plays such an important role in multivariable calculus and physics.

At its core, the dot product tells us how much one vector points in the direction of another. This idea shows up naturally in concepts like projection, work, and directional change.

Key idea:
For vectors u and v, the dot product is
u·v = |u||v| cos θ,
where θ is the angle between them.

This formula explains why the dot product captures alignment between vectors, and why it becomes zero when vectors are orthogonal.

Until next time – let’s keep things simply connected!

#mathematics #dotproduct #multivariable #calculus #physics #simply #connected