11.1 Vectors in the Plane

 Quantities that have magnitude but not direction are called scalars. Ex: Area, volume, temperature, time, etc.  Quantities such as force, acceleration or velocity that have direction as well as magnitude are represented by directed line segments, called vectors. A B initial point terminal point  The length of the vector is called the magnitude and is denoted by Definitions

 A vector is in standard position if the initial point is at the origin. x y  The component form of this vector is:  Vectors are equivalent if they have the same length and direction (same slope). then the component form of is:  If are initial and terminal points of a vector, P Q (c,d) (a,b) v (a-c, b-d) x

P Q (-3,4) (-5,2) The component form of is: v (-2,-2) The magnitude is Example

i and j If then v is a zero vector : are called the standard unit vectors. The magnitude ofis: If then v is a unit vector.

Vector sum: Vector difference Scalar Multiplication: Negative (opposite): Vector Operations

v v u u u+v u + v is the resultant vector. v v u u u-v u - v is the resultant vector. Parallelogram Law

i j are called horizontal and vertical components of v v is called a linear combination of i and j Any vectors can be written uniquely in terms of standard unit vectors : v (measured counterclockwise) with the positive x -axis then v can be written as If v is any nonzero vector that makes an angle Linear Combination