1
VECTORS
DEF
:
A vector
is a quantity that has both
magnitude and direction.
DEF
:
A scalar
is a quantity that has magnitude
but NO
direction.
Ex
.
Vectors
Scalars
Force
Temperature
Velocity
Time
Displacement
Mass
Momentum
Speed
Vector Notation
A
– Boldface letters
A
G
 Arrow above letter
A – Magnitude of vector
A
A vector is defined graphically by an arrow
whose length is proportional to the magnitude of
the vector quantity.
The direction of the arrow
points in the direction of the vector quantity.
Adding Vectors Graphically
Consider adding two vectors A and B
graphically.
The two vectors are shown below.
q
A
B
A
B
R
f
f
1.
Select an appropriate scale. (Ex. 20 cm
= 5 N)
2. Draw vector
A
to scale and in the proper
direction.
3. Draw vector
B
to the same scale with its
tail at the tip of
A
and in the proper
direction.
4. The resultant vector
R
=
A
+
B
is the
vector drawn from the tail of vector
A
to
the tip of vector
B
.
5.
Calculate the magnitude of the resultant
vector
R
using the selected scale and
measure its direction with a protractor.
6.
This same process applies if you add
more than two vectors.
This method of adding vectors graphically is also
referred to as the
headtotail method, analytical
method, and geometric method.
Properties of Vectors
1
.
A
+
B
=
B
+
A
(commutative Law)
2.
A
+
(B
+
C)
=
(A
+
B)
+
C
(associative Law)
3.
A
+
(A)
=
0
(Negative of a vector)
4.
A
–
B
=
A
+
(B)
(vector subtraction)
5.
B
= s
A
(vector multiplied by a scalar)
A
B
A
B
B
A
A + B
B + A
(1)
A
B
C
B
C
(2)
A
 A
= 0
(3)
A
B
 B
A
B
A  B
(4)
(5)
B
= s
A
is a vector with magnitude
│
s
│
A and is
parallel to
A
if s is positive and antiparallel if s is
negative.
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 Spring '11
 Luna
 Acceleration, Force, Mass, Momentum, Velocity, Ri, Ry, θ. Ax

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