In Exercises 39–46, find the unit vector that has the same direction as the vector v.


v = -5j

Key Concepts

Unit Vector

A unit vector is a vector that has a magnitude of one and indicates direction. To find a unit vector in the same direction as a given vector, you divide the vector by its magnitude. This process normalizes the vector, allowing it to retain its direction while having a standardized length.

Magnitude of a Vector

The magnitude of a vector is a measure of its length and is calculated using the formula √(x² + y² + z²) for three-dimensional vectors. For a two-dimensional vector like v = -5j, the magnitude is simply the absolute value of its components. Understanding how to compute the magnitude is essential for normalizing the vector to create a unit vector.

Direction of a Vector

The direction of a vector indicates the path along which it acts and is often represented by the angle it makes with a reference axis. In the case of the vector v = -5j, it points directly downward along the y-axis. Recognizing the direction is crucial when finding a unit vector, as it ensures that the resulting unit vector maintains the same orientation.