Final answer:
In mathematics, the dot product is commutative, so the statement that v · u equals u · v for any two vectors in ℝ³ is true.
Step-by-step explanation:
The dot product (also known as the scalar product) operation between two vectors in mathematics is commutative. This means that for any vectors u and v in ℝ³ (the three-dimensional real number space), it holds that v · u is equal to u · v. The result is a scalar quantity, and the order of multiplication does not affect the outcome. The commutative property holds true because the dot product is defined as the sum of the products of the corresponding components of the two vectors, which does not depend on the order of the vectors.
To illustrate, let u = (u1, u2, u3) and v = (v1, v2, v3). Then the dot product u · v = u1*v1 + u2*v2 + u3*v3, and similarly v · u = v1*u1 + v2*u2 + v3*u3. As we can see, switching the order of u and v does not change the result. Therefore, the answer is:True