ME 221
Statics
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Vectors; Vector Addition
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Define scalars and vectors
Vector addition, scalar multiplication
2-D trigonometry
Vector components
Law of cosines
Law of sines
Problems
ME221
Lecture 2
2
Scalars and Vectors
• Scalar is a quantity that is represented by a
single number
– examples: mass, temperature, angle
• Vectors have both magnitude and direction
– Examples: velocity, acceleration, force
– Acceleration due to gravity is down not up!
ME221
Lecture 2
3
VECTORS
Line of Action
Magnitude
y
Vector
A or A

Direction
x
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Lecture 2
4
Vectors
• Vectors are equal when they have the same
magnitude and direction
B
A
=
• Vectors add by the parallelogram rule
A
+
ME221
B
A
=
Lecture 2
B
C
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More on Vectors
• Vectors are communative
A+B=B+A
B
A
C
A
B
• Vectors are associative
(A + B) + C = A + (B + C)
ME221
Lecture 2
6
Subtraction of Vectors
In order to subtract vectors, first we must understand that if we
multiply a vector by (-1) we get a vector equal in length but exactly
opposite in direction.
A
-A
Then we see that B - A = B + (-A)
B
A
So if we have D = B - A
D
This looks like this:
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-A
Lecture 2
7
Adding More Than Two Vectors
B
A
A
B
A+B

C
D
C
D = A+B+C
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Lecture 2
8
Law of Cosines
This will be used often in balancing forces
g
b
a
b
a
c
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Lecture 2
9
Law of Sines
Again, used throughout this and other classes
Start with the same triangle:
g
b
a
b
a
c
ME221
Lecture 2
10
Example
Determine by trigonometry the
magnitude and direction of the
resultant of the two forces shown
25o
200 lb
ME221
45o 300 lb
Lecture 2
Note: resultant of two
forces is the vectorial
sum of the two vectors
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