i. On a chessboard a king sits at a position of +12 em from the lower left corner. A knight is +5.0cm from the same corner along the same straight line. What is the displacement from the king to the knight?(3) Draw a picture for full marks The displacement is -7 cm Ad=+12-(+5.0)=

Here's the solution:<br /><br />1. **Understanding Displacement:** Displacement is a vector quantity, meaning it has both magnitude (size) and direction. It represents the change in position of an object. In this case, we're looking for the displacement *from* the king *to* the knight.<br /><br />2. **Setting up the Problem:** Let's consider the lower left corner of the chessboard as our origin (0 cm). The king is at +12 cm, and the knight is at +5.0 cm. We want to find the displacement from the king to the knight.<br /><br />3. **Calculating Displacement:** The displacement is the final position (knight's position) minus the initial position (king's position).<br /><br /> Displacement = (Knight's Position) - (King's Position)<br /> Displacement = (+5.0 cm) - (+12 cm)<br /> Displacement = -7.0 cm<br /><br />4. **Interpreting the Result:** The negative sign indicates the direction. A displacement of -7.0 cm means the knight is 7.0 cm *behind* the king relative to the lower-left corner of the chessboard. In other words, to get from the king to the knight, you would move 7.0 cm towards the lower-left corner.<br /><br />**Diagram:**<br /><br />```<br /> 0 cm +5 cm +12 cm<br /> |-------------------------------------------K-----------------------N---|<br /> Lower Left Corner <br />```<br /><br />Where:<br /><br />* K represents the King's position.<br />* N represents the Knight's position.<br /><br /><br />Therefore, the displacement from the king to the knight is $\boxed{-7.0 \text{ cm}}$.<br />