Vector A quantity that shows both magnitude and direction.

Vector Examples  Position  Displacement  Velocity  Acceleration  Force  Momentum

Vectors (One dimension)  vector = +/- scalar directionmagnitude +: right, up, north, east-: left, down, south, west ex: +3.9 m/s, -5.2 N, -76 m

Vectors (Two Dimensional)  v = vector v = magnitude, angle direction = angle direction = angle direction = magnitude = magnitude (called magnitude-angle form)  A, v, d 1, F R  In a book a vector is represent as a bold letter, e.g. A  Examples: v=3.4 m/s, 25º = º = 3.4 m/s F=8.2 N, -64º = º = 8.2 N d=47 m, 15º N of W = 47 15º N of W = 47 m angle direction 25° -64° 15° N of W

Graphically Representing a Vector θ A A=A, θ A=magnitude of vector A = length of vector A The tail of the vector The head (tip) of the vector A vector can be moved; as long as the magnitude and direction are the same the vector is unchanged. A

Negative of a Vector (Opposite Direction of a Vector) θ+180° -A A=A, θ A = 5.6 m/s, 60°-A= 5.6 m/s, 240° -A=A, θ±180 The negative of a vector has the same magnitude as the original vector with a 180° difference in direction A Same magnitude, but a direction difference of 180°

Scaling a Vector  A=A, θ  aA=aA, θ  (To scale a vector, only multiply the magnitude of the vector by the factor; the angle is unchanged).  A=4.0 m/s, 23°  2A=8.0 m/s, 23° Twice as long as the original vector, but in the same direction.

Vector Direction Conventions 0º0º 90º 180º 270º -270º -180º -90º E S N W E N W S E of N N of E S of E E of S W of S S of W N of W W of N

Example of Vector Direction Conventions A A=3.4 km, 57° B B = 7.9 m/s, 18° S of W

Component Form of a Vector v vxvx vyvy v

Example of the Component Form of a Vector v 4.0 m/s 3.0 m/s v

Conversion of a Vector in Magnitude-Angle Form to Component Form

Conversion of Component Form to Magnitude-Angle Form of a Vector v magnitude of v direction of v adjust angle for quadrant, If necessary Example: