Section 81: Vectors

1
Section 8-1 Vectors
A vector is any quantity with magnitude (size)
and amplitude (direction). Magnitude is the
distance from initial point, A, to terminal
point, B.
2
Standard Position
A vector in standard position has its initial
point at the origin. The amplitude of the vector
is the angle the vector makes with the positive
x-axis.
3
Finding the magnitude and amplitude.

• v v32 42
• 5
• ? tan-1 4.0 3.0
• tan-1(1.33)
• 49

4
Parallel Vectors

• Parallel vectors have the same or opposite
  direction, or amplitude.
• They do not necessarily have the same length, or
  magnitude.

5
Equal vectors.

• Equal vectors have the same magnitude and
  amplitude.

6
Find the magnitude and direction of each vector
to show they are equal.

• Magnitude v(4-0)2 (-7-0)2 v65
• v(6-2)2 (-2-5)2 v65
  
• Amplitude tan-1(-7/4)
• tan-1(-1.75)
• (ref. angle) -60
• ? 300

7
Vectors have a vertical and a horizontal
component.
(vert. comp.)
(horiz. comp.)
8
Horizontal and Vertical components.

• h acos ?
• v asin ?
• (x,y)(acos?, asin?)

9
Describing a vector using an ordered pair.

• This vector has the ordered pairOP(20cos120,
  20sin120)
• OP(-10, 17.3)

10
Describing a Vector Direction.

• Use the compass directions to describe the
  direction of each vector.

40 North of East
60 South of West
11
Finding the distance and direction.

• A plane flies west for 40 miles and then south
  for 25 miles.
• The result can be described by the ordered pair
  (-40, -25).
• Find the distance
• Find the direction

47.1 miles
32 S of W
12
The velocity of the canoe is the vector sum of
the paddlers and the stream.

• The canoe paddles directly away from shore at a
  rate of 5 mph.
• The current travels downstream at rate is 8 mph.
• Find the resultant velocity of the canoe.
• Find the resultant direction.

9.4 mph
58 downstream
13
Vocabulary

• One Newton (N) is the force needed to accelerate
  a 1 Kg mass at a rate of one meter per second.

14
Combined Forces

• Two forces are acting on an object.
• One force is 12N south and the other is 5N east.
• What is the magnitude and amplitude of the
  resultant vector?

Magnitude 13N Amplitude 292.6 or 67.8
South of East
15
The resultant vector

• Vectors a and b can be added together.
• This is known as the resultant vector ab.
• We will discuss this tomorrow.

16
Homework

• Page 417
• 29-33, 37-38, 40-44