1) Make sure you understand the difference between a vector and the magnitude of a vector.
In the following, consider vectors in 2 dimensions: The magnitude of
V
3
=
V
1
+
V
2
depends on
the orientation of the vectors
V
1
and
V
2
!
Examples:

V
3
=V
1
+V
2


V
3
=V
1
V
2

V
1
V
2
V
2
V
1
V
3
V
3

V
3
<V
1
+V
2

V
2
V
1
V
3
2, 3, 4) Remember:
A

B
=
A +
(

B
)
If you know the components Ax, Ay and Bx, By of the vectors
A
and
B
, then you get the
components Cx and Cy of the vector
C
=
A
+
B
from: Cx = Ax+Bx, and Cy =
Ay + By.
If you know the components Ax and Ay of a vector
A
then you know its magnitude 
A
:

A
 = squareroot of (Ax
2
+ Ay
2
) You know this already from geometry: The ‘Pythagorean
relation’:
c
a
b
c
2
= a
2
+ b
2
(think of a and b as the x and y components of
a vector along c with magnitude c)
β
a
b
c
a = c * cos
β
(‘a’ is the cozy side of
β
)
b = c * sin
β
Use this information to solve problems 2, 3, and 4.
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View Full Document5. Remember: The magnitude of a vector
V
is the ‘length’ of the vector. Above you find how
to calculate the magnitude in 2 dimensions (use the Pythagorean relation 
V
 = x
2
+ y
2
.
In 3 dimensions you can simply use 
V
 = x
2
+ y
2
+ z
2
(see text book.)
If you are given a vector as
V
= x*
i
+ y*
j
+ z*
k
, then x,y,z are the x, y, and z components of
the vector. The magnitude 
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 Spring '08
 ROGERS
 Physics, Vector Space, Acceleration, Velocity, initial velocity, xdirection

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