1. The problem is to evaluate the vector \( \left( \frac{1}{2}, -3 \right) \) and understand its components. 2. A vector in 2D is written as \( \left( x, y \right) \), where \( x \) is the horizontal component and \( y \) is the vertical component. 3. Here, the vector is \( \left( \frac{1}{2}, -3 \right) \), meaning the horizontal component is \( \frac{1}{2} \) and the vertical component is \( -3 \). 4. This vector points half a unit to the right (positive direction) and 3 units down (negative direction). 5. The vector can be used in various applications such as physics for displacement or in algebra for coordinate points. 6. No further simplification is needed as the components are already in simplest form. Final answer: The vector is \( \left( \frac{1}{2}, -3 \right) \) with horizontal component \( \frac{1}{2} \) and vertical component \( -3 \).