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(c)
12
0
dd
⋅=
GG
since
ˆˆ
ij=0
.
⋅
The two vectors are perpendicular to each other.
(d)
1
2
(/
4
)(
)
/
40
⋅
=
G
G
, as in part (c).
(e)
1
2
1
2
ˆ
(j i)=
k
dd d
d
d
d
×=
−
×
, in the +
z
direction.
(f)
21
2
1
1
2
ˆ
(i j) =
k
d
d
d
−
× −
, in the
−
z
direction.
(g) The magnitude of the vector in (e) is
.
(h) The magnitude of the vector in (f) is
.
(i) Since
1
2
ˆ
(
/ 4)
(
/ 4)k
d
d
G
, the magnitude is
/4.
(j) The direction of
1
2
ˆ
(
/ 4)
(
/ 4)k
d
d
is in the +
z
direction.
56. The two vectors
1
d
G
and
2
d
G
are given by
11
2
2
j and
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics

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