VECTORSVECTORSVECTORSVECTORS

Describing pathsDescribing paths

VECTOR: line segment with…

i. Direction (an angle)

ii. Magnitude ||v|| = length of vector (distance)

EX: AB

Point A is the origin or initial pointPoint B is the endpoint or terminal point

A

B

A

B

Basic terminology and notation:

v

Let v = A B

ZERO VECTOR: ||v|| = 0

EQUAL VECTORS: Same magnitude & direction

Also Equal

NOT EQUAL

NOT EQUAL

VECTOR SUM:

XY + YZ = XZ

X

Y

Z

Opposite vectors:

v - w

v

w

-w

Notation v = < 3, 4 > 3 right, 4 up from initial point

w = < ?, ? >V = < ?, ? >

EX 1: Graph 2v -3w

a

b|| V || = ?

22 ba || v || =

Magnitude or length

APPLICATION PROBLEMS

• Write a vectors representing the situation and draw the resulting trip.

• A small motorboat in still water maintains a speed of 10 mph. When the boat heads directly across a river it is perpendicular to the 4mph current. At what speed will the boat actually be travelling?

The Resultant Velocity is the sum of the two

Velocities

current

boat

VECTOR ANGLE

EXAMPLE:

Sketch a vector 60 degrees North of East

THE DOT (scalar) PRODUCT

v · w = a1 a2 + b1 b2

v = <a1, b1> w = <a2 , b2>

EXAMPLES:

FIND:

v · w w · v

v · v

w · w

v = <2 , 3 > w = <5 ,3>