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(c) If the starting point is (0,
a
, 0) with the corresponding position vector
ˆ
j
a
, the
diametrically opposite point is (
a
, 0
, a
) with the position vector
ˆˆ
ik
aa
+
. Thus, the
vector along the line is the difference
ˆ
ij
k
a
−+
.
(d) If the starting point is (
a
,
a
, 0) with the corresponding position vector
i
j
+
, the
diametrically opposite point is (0, 0
, a
) with the position vector
ˆ
k
a
. Thus, the vector
along the line is the difference
ˆ
k
a
−−
+
.
(e) Consider the vector from the back lower left corner to the front upper right corner. It
is
ˆ
j
k
.
aaa
++
We may think of it as the sum of the vector
a
#
i
parallel to the
x
axis and
the vector
j
k
##
+
perpendicular to the
x
axis. The tangent of the angle between the
vector and the
x
axis is the perpendicular component divided by the parallel component.
Since the magnitude of the perpendicular component is
22
2
a
+=
and the
magnitude of the parallel component is
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 Spring '08
 Any
 Physics

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