Lecture 2
Vectors.
What is a vector?
•A
scalar
quantity is one that is represented
by a single number.
(Eg: Mass, length, time,
temperature, volume.)
vector
is a quantity which has both magnitude
and direction. (Eg: Displacement, velocity, force.)
Direction: something like “Makes an angle of 36
°
with the horizontal as measured CCW”
Notation:
A
or A (or
)
Magnitude (how long): 
 or
•
Equal vectors
:
Moving from P to Q, and from R to S:
x Q
x Q
P x
P x
x S
x S
R x
R x
A
B
A
=
B
Vector basics
x Q
x Q
P x
P x
A
A
•
Opposite vectors
:
Moving from P to Q, and from Q to P.
•
Unit vector
(
Â
):
magnitude equals one.
A
= A
Â
Vector addition
:
Moving from P, to Q, to R
x Q
x Q
P x
P x
x R
x R
A
B
C
A
B
C
=

C
=
+
Vector subtraction
:
It’s an addition!
−
B
=
+(
−
)
Visually: What do I
have to add to B to
get A?
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View Full DocumentACT: Vector addition
All the vectors below have the same magnitude. Which of
the following arrangements will produce the largest
resultant when the two vectors are added?
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 Fall '06
 Johnson
 Physics, Vectors, Vector Space, Dot Product, Mass, ax bx, Ax Bz

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