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Chapt. 3 Vectors and Trigonometry 33
c) Say that
n
is any number greater than 1. Find the numerical value of vector sum of the
vectors
v
A
=
s
i
v
A
i
and prove why it is that value.
HINT:
Imagine rotating the set of vectors by 360
◦
/n
. The
sum vector should rotate too—but shouldn’t it also be in the same place as before?
d) Now say that
n
= 1. The only vector in the set is
v
A
1
. What is the vector sum in this case?
Why is it not the same in general as the vector sum found in the part (c) answer?
003 qfull 00790 3 5 0 tough thinking: vector rotational transformations
Extra keywords:
One needs a lot of hints for 20minute test situation
6. Say you have a vector speci±ed by
v
r
= (
x,y
) in relative to Cartesian
x

y
axes. Now create new
x
′

y
′
axes by rotating the old axes by
θ
counterclockwise. The vector
v
r
has
NOT
moved: it is
still the same magnitude and physical direction. But relative to the new axes it is speci±ed by
(
x
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 Fall '06
 Buchler
 Physics

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