A

To find the unit vector in the direction of a given vector, we first need to know the components of the vector. Let's denote the vector as \( extbf{A} = (x, y) \). The unit vector in the direction of \( extbf{A} \) is obtained by dividing each component of \( extbf{A} \) by its magnitude.

Step 1: Calculate the magnitude of the vector \( extbf{A} \):
\( ||\textbf{A}|| = \sqrt{x^2 + y^2} \)

Step 2: Formulate the unit vector \( \hat{\textbf{A}} \):
\( \hat{\textbf{A}} = \frac{1}{||\textbf{A}||}(x, y) = \left( \frac{x}{||\textbf{A}||}, \frac{y}{||\textbf{A}||} \right) \)

Therefore, the unit vector is calculated based on the given vector components.