Physics
Instructor: Dr. Tatiana Erukhimova
Vectors
Vectors
Vector quantity has
direction as well as
magnitude
1.On a diagram, draw one of the
vectors – call it D1 - to scale.
2. Next draw the second vector, D2, to
scale, placing its tail at the tip of the
first vector and being sure its
direction is correct.
3. The arrow drawn from the tail of the
first vector to the tip of the second
represents the sum, or resultant, of
the two vectors.
 
 
V1  V2  V2  V1 (commutative law)

 
 

V1  (V2  V3 )  (V2  V1 )  V3 (associative law)
No vector is ever negative in the sense of its
magnitude: the magnitude of every vector
is positive
Resolving the vector into its components
Vx  V1x  V2 x
Vy  V1 y  V2 y
Adding Vectors by Components
1. Draw a diagram
2. Choose x and y axes. Choose them in a way that make
your work easier. (E.g. choose one axis along the
direction of one of the vectors so that the vector will
have only one component).
3. Resolve each vector in x and y components
4. Calculate each component using sine and cosine. Be
careful with signs: any component that points along the
negative x or y axis gets a negative sign.
5. Add the x components together to get the x component
of the resultant. Similar for y:
Vx=V1x+V2x+…
Vy=V1y+V2y+…
6. If you want to know the magnitude and direction of
the resultant vector,
V  V V
2
x
2
y
tan  
Vy
Vx
Mail carrier’s displacement
A rural mail carrier leaves the post office
and drives 22.0 km in a northerly
direction to the next town. She then drives
in a direction 60.00 south of east for 47.0
km to another town. What is her
displacement from the post office?
You want to measure
the height of a
building. You stand
2m away from a 3m
pole and see that it’s
“in line” with the top
of the building. You
measure 16 m from
the pole to the
building.
What is the height of
the building?
16 m
Three vectors are shown in the Figure. Their magnitudes are



A  44, B  26.5, C  31;
1  280 ,  2  560
y

A

B
2
1
x

C
Determine the sum of the three vectors. Give the resultant in
terms of
a) components
b) magnitude and angle with x axis


What is the sum of the two vectors a and b ?
y

b
2
1

a
x
An airplane trip involves three legs, with two stopovers.
The first leg is due east for 620 km; the second leg is
southeast (450) for 440 km; and the third leg is at 530
south of west for 550 km. What is the plane’s total
displacement?
Three horizontal ropes pull on
 stuck in the ground,
 a large stone
producing the vector forces A, B , and C.
Find the magnitude and direction of a fourth force on the stone that
will make the vector sum of the four forces zero.

B (80 N )
y
30o

A(100 N )
30o
53o

C (40 N )
x
 

a) Express the vectors F1, F2 , and F3 in terms of their
components.
y

F2
2
3

F3
b) Find



F1  F2.  F3
x

F1
Have a great day!
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