\mathbf{u} \cdot \mathbf{v} = 3(-1) + 4(2) = -3 + 8 = 5

Mon, 04 May 2026 08:46:55 +0000

Understanding the Dot Product: U ⋅ V = 5 Explained When working with vectors in mathematics and physics, the dot product (often written as u · v) is a powerful tool that reveals important geometric and directional relationships between two vectors. One of the simplest yet illustrative calculations involves evaluating u · v = 3(-1) + 4(2) = -3 + 8 = 5. In this article, we’ll break down what this expression means, how the dot product works, and why computing the dot product this way yields a clear result. ### What Is the Dot Product? The dot product is an operation that takes two vectors and produces a scalar — a single number that encodes how much one vector points in the direction of another. For two 3-dimensional vectors u and v, defined as:
- u = [u₁, u₂, u₃]
- v = [v₁, v₂, v₃]