The unit vector in the direction of the vector $(6, 8)$ is $(0.6, 0.8)$.

To compute the unit vector for a given vector, we first need to find the magnitude (or length) of the original vector. The magnitude of a vector $(x, y)$ is determined using the formula:

For the vector $(6, 8)$, we calculate its magnitude as follows:

Once we have the magnitude, we can obtain the unit vector by dividing each component of the original vector by its magnitude. This process effectively scales the vector down to a length of 1 while preserving its direction. For the vector $(6, 8)$, we perform the following calculations:

Thus, the unit vector in the direction of $(6, 8)$ is $(0.6, 0.8)$.

Unit vectors are particularly useful in various fields of mathematics and physics, as they provide a means to express direction without the need to consider magnitude. For instance, in physics, unit vectors are commonly employed to represent the directions of forces or velocities. By mastering the process of finding and utilizing unit vectors, you can simplify numerous problems and enhance the clarity of your calculations.