which of the following best represents\n$\\vec{a} - \\vec{b} = \\vec{c}$?

Explanation:

Step1: Identify vector directions

Vector $\vec{A}$ points upward and vector $\vec{B}$ points to the left.

Step2: Rewrite the vector equation

Rearrange the subtraction into an addition of the negative vector. $$\vec{C} = \vec{A} + (-\vec{B})$$

Step3: Determine the negative vector

Since $\vec{B}$ points left, $-\vec{B}$ must point to the right.

Step4: Apply the tip-to-tail method

Place the tail of $-\vec{B}$ at the tip of $\vec{A}$.

Step5: Identify the resultant vector

The vector $\vec{C}$ starts at the tail of $\vec{A}$ and ends at the tip of $-\vec{B}$.

Step6: Evaluate the given diagrams

The first diagram shows $\vec{A}$ (up) followed by a rightward vector (which is $-\vec{B}$), resulting in $\vec{C}$ pointing down-left.

Answer:

The first diagram (bottom-left) best represents $\vec{A} - \vec{B} = \vec{C}$.