Final answer:
The defined matrix multiplication in the context of vectors is the dot product (scalar product), which yields a scalar value based on the magnitudes of the vectors and the cosine of the angle between them.
Step-by-step explanation:
In mathematics, specifically in vector calculus, there are two distinct kinds of vector multiplication, each with its own properties and applications. When two vectors are multiplied concerning scalar multiplication, the result is a scalar product, also known as the dot product. This operation yields a scalar and utilizes the magnitudes of the two vectors and the cosine of the angle between them. For example, two orthogonal vectors (at a 90-degree angle to each other) will have a scalar product of zero because the cosine of 90 degrees is zero. The scalar product is important in physics, particularly in the definition of work and energy.
On the other hand, the vector product or cross product results in a vector and is used to describe quantities such as torque in physics. The cross product depends on both the magnitude of the vectors and the sine of the angle between them. Because the cross product is a vector, it has both magnitude and direction, and it is orthogonal to the plane formed by the original vectors. Unlike the dot product, the cross product is anti-commutative, meaning that reversing the order of multiplication results in the negation of the vector.
Therefore, the correct answer to the question is c) Dot product, which is the form of vector multiplication that is specifically defined by scalar multiplication resulting in a scalar value.