1. Vectors in Plane Objectives of this Section Graph Vectors Find a Position Vector Add and Subtract Vectors Find a Scalar Product and Magnitude of a Vector Find a Unit Vector Find a Vector from its Direction and Magnitude Work With Objects in Static Equilibrium

2. A vector is a quantity that has both magnitude and direction. Vectors in the plane can be represented by arrows. The length of the arrow represents the magnitude of the vector. The arrowhead indicates the direction of the vector.

3. P Q Initial Point Terminal Point Directed line segment

4. If a vector v has the same magnitude and the same direction as the directed line segment PQ, then we write

5. The vector v whose magnitude is 0 is called the zero vector, 0. if they have the same magnitude and direction. Two vectors v and w are equal, written

6. Initial point of v Terminal point of w Vector Addition

7. Vector addition is commutative. Vector addition is associative.

8. Multiplying Vectors by Numbers

9. Properties of Scalar Products

10. Use the vectors illustrated below to graph each expression.

15. Let i denote a unit vector whose direction is along the positive x-axis; let j denote a unit vector whose direction is along the positive y-axis. If v is a vector with initial point at the origin O and terminal point at P = (a, b), then

16. a P = (a, b) v = ai + bj b

17. The scalars a and b are called components of the vector v = ai + bj.

19. O v = 5i + 3j

20. Equality of Vectors Two vectors v and w are equal if and only if their corresponding components are equal. That is,

24. Unit Vector in Direction of v For any nonzero vector v, the vector is a unit vector that has the same direction as v.

25. Find a unit vector in the same direction as v = 3i - 5j.