ANSWERS
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PRE
Lesson 8.4 Vectors
Objectives:
•To define a
•To perform algebraic operations on vectors.
VECTOR
A vector in the plane is a line segment with
an assigned direction and magnitude.
• We sketch a vector as shown
with an arrow to specify the
direction.
• We denote this vector by AB
INITIAL AND TERMINAL
POINTS
Point A is the initial point of the
vector AB
Point B is the terminal point of
the vector.
COMPONENTS
We represent v as an ordered pair of real
numbers. v = <a, b>
where:
• a is the horizontal component of v.
• b is the vertical component of v.
LENGTH OF A VECTOR
The magnitude or length of a vector
v  a, b
| v | a  b
2
2

If a vector v is represented in the
plane with initial point P(x1, y1)
and terminal point
Q(x2, y2), then
v   x2  x1 , y2  y1 
v   x2  x1 , y2  y1 
v   3  ( 2),7  5
v  5, 2
PROPERTIES OF VECTORS
ALGEBRAIC OPERATIONS
ON VECTORS
a) u + v   2   1 ,  3  2  1, 1
b) u – v   2   1 ,  3  2   3, 5
c) 2u   2  2, 2  3   4, 6
d) –3v  3  1, 3  2   3, 6
e) 2u + 3v   4   3 ,  6  6  1,0
 4, 6 3,6
Classwork: Polar Coordinate/Vector Worksheet:
17-25 all