How do you write the vector difference of m and n?

The vector difference of \( \mathbf{m} \) and \( \mathbf{n} \) is written as \( \mathbf{m} - \mathbf{n} \).

In more detail, vectors are quantities that have both magnitude and direction. When we talk about the vector difference, we are essentially subtracting one vector from another. If you have two vectors, \( \mathbf{m} \) and \( \mathbf{n} \), the vector difference \( \mathbf{m} - \mathbf{n} \) represents a new vector that points from the tip of \( \mathbf{n} \) to the tip of \( \mathbf{m} \).

To subtract vectors, you subtract their corresponding components. For example, if \( \mathbf{m} = (m_1, m_2) \) and \( \mathbf{n} = (n_1, n_2) \) in a 2-dimensional space, the vector difference \( \mathbf{m} - \mathbf{n} \) is calculated as:
\[ \mathbf{m} - \mathbf{n} = (m_1 - n_1, m_2 - n_2) \]

This means you subtract the first component of \( \mathbf{n} \) from the first component of \( \mathbf{m} \), and the second component of \( \mathbf{n} \) from the second component of \( \mathbf{m} \). The result is a new vector that shows the relative position of \( \mathbf{m} \) with respect to \( \mathbf{n} \).

Understanding vector subtraction is important in various applications, such as physics, engineering, and computer graphics, where you often need to find the difference between two points or directions.