6.1 Vectors in the Plane

What you’ll learn about Two-Dimensional Vectors Vector Operations Unit Vectors Direction Angles Applications of Vectors … and why These topics are important in many real-world applications, such as calculating the effect of the wind on an airplane’s path.

Directed Line Segment

Two-Dimensional Vector

Initial Point, Terminal Point, Equivalent

Head Minus Tail (HMT) Rule

Magnitude

Example Finding Magnitude of a Vector

Example Finding Magnitude of a Vector

Vector Addition and Scalar Multiplication

Example Performing Vector Operations

Example Performing Vector Operations

Unit Vectors

Example Finding a Unit Vector

Example Finding a Unit Vector

Standard Unit Vectors

Resolving the Vector

Example Finding the Components of a Vector

Example Finding the Components of a Vector

Example Finding the Direction Angle of a Vector

Example Finding the Direction Angle of a Vector

Example Finding the Direction Angle of a Vector

Example Finding the Direction Angle of a Vector

Velocity and Speed The velocity of a moving object is a vector because velocity has both magnitude and direction. The magnitude of velocity is speed.