The problem presented asks to convert the vector $\overrightarrow{AB} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$ into its analytical form. The analytical form of a vector is typically expressed in terms of the unit vectors $\hat{i}$ and $\hat{j}$, which correspond to the x- and y-components, respectively.

For the vector $\overrightarrow{AB} = \begin{pmatrix} 2 \\ 3 \end{pmatrix}$:

• The x-component is 2, so the term for this is $2\hat{i}$.
• The y-component is 3, so the term for this is $3\hat{j}$.

Thus, the analytical form of the vector is: $\overrightarrow{AB} = 2\hat{i} + 3\hat{j}$

Now, comparing this result with the given options:

• Option c: $\overrightarrow{AB} = 2\hat{i} + 3\hat{j}$ is the correct answer.

Would you like further clarification, or details on vector notation? Here are 5 related questions to consider:

1. How do you calculate the magnitude of a vector from its components?
2. How do you add or subtract two vectors in component form?
3. What is the scalar (dot) product of two vectors?
4. How can you represent a 3D vector in analytical form?
5. What is the relationship between unit vectors and vector components?

Tip: When expressing vectors in analytical form, always match the x-component with $\hat{i}$ and the y-component with $\hat{j}$.