To express CD in terms of a, let’s analyze the diagram carefully.

Key Observations:

1. $\vec{AB} = \mathbf{a}$, so vector $\vec{AB}$ represents the displacement from $A$ to $B$.
2. The diagram shows that vector $\vec{CD}$ has the same direction and magnitude as vector $\vec{AB}$, but it points in the opposite direction.

Steps:

• If a vector points in the opposite direction, it is the negative of the original vector.
• Therefore, $\vec{CD}$ is the reverse of $\vec{AB}$.

Final Answer:

$\vec{CD} = -\mathbf{a}$

Let me know if you'd like a breakdown of vector directions or further clarifications!

Related Questions:

1. How do you determine if two vectors are parallel?
2. What does it mean for a vector to have a negative sign?
3. How can vectors be represented algebraically in coordinates?
4. How do you calculate the magnitude of a vector?
5. What are some real-life examples of opposite vectors?

Tip:

When vectors point in opposite directions but have the same magnitude, the vectors are negatives of each other.