The problem asks to find the correct graphical representation of the vector sum $\vec{A} + \vec{B} = \vec{C}$. In the image, four options (A, B, C, D) display possible arrangements of vectors $\vec{A}$, $\vec{B}$, and $\vec{C}$ in a triangle format to show the sum of the vectors.

Explanation:

To correctly represent vector addition $\vec{A} + \vec{B} = \vec{C}$, the vectors should follow the head-to-tail method. This means the tail of vector $\vec{B}$ should start at the head of vector $\vec{A}$, and the resulting vector $\vec{C}$ should be drawn from the tail of $\vec{A}$ to the head of $\vec{B}$.

Analyzing the Options:

• Option A shows the correct head-to-tail method for vector addition. Here, $\vec{A}$ is directed to the left, and $\vec{B}$ is directed upward, forming a triangle where the vector $\vec{C}$ completes the sum from the tail of $\vec{A}$ to the head of $\vec{B}$.
• Option B, C, and D do not follow the correct head-to-tail arrangement of vectors for vector addition.

Thus, Option A is the correct representation of the vector addition $\vec{A} + \vec{B} = \vec{C}$.

Would you like a further breakdown of the vector addition process?

Related Questions:

1. What is the head-to-tail method in vector addition?
2. How can you calculate the magnitude of $\vec{C}$ in terms of $\vec{A}$ and $\vec{B}$?
3. What happens if $\vec{A}$ and $\vec{B}$ are perpendicular vectors?
4. Can vectors be added algebraically if they have components along different axes?
5. How does the direction of $\vec{C}$ relate to the directions of $\vec{A}$ and $\vec{B}$?

Tip:

When working with vector diagrams, always start by aligning vectors head-to-tail for proper visualization of the sum.