In Exercises 22–24, sketch each vector as a position vector and find its magnitude. v = -3j

Key Concepts

Position Vectors

A position vector represents a point in space relative to an origin. In a two-dimensional Cartesian coordinate system, a position vector is expressed in terms of its components along the x and y axes. For example, the vector v = -3j indicates a point that is 3 units in the negative y-direction, with no displacement along the x-axis.

Magnitude of a Vector

The magnitude of a vector is a measure of its length and is calculated using the Pythagorean theorem. For a vector expressed in component form as v = ai + bj, the magnitude is given by the formula |v| = √(a² + b²). In the case of v = -3j, the magnitude is simply the absolute value of the y-component, which is 3.

Unit Vectors

A unit vector is a vector that has a magnitude of one and indicates direction. It is often used to represent the direction of a vector without regard to its magnitude. To convert a vector into a unit vector, you divide the vector by its magnitude. For the vector v = -3j, the unit vector would be -j, indicating the same direction but with a magnitude of 1.