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55. The two vectors are given by
ˆˆ
ˆ
ˆ
8.00(cos130 i sin130 j)
5.14i 6.13 j
ˆ
ˆ
i
j
7.72i 9.20 j.
xy
A
BB B
=°
+
°
=
−
+
=+=
−
−
G
G
(a) The dot product of 5
AB
⋅
G
G
is
5
5( 5.14i 6.13 j) ( 7.72i 9.20 j)
5[( 5.14)( 7.72) (6.13)( 9.20)]
83.4.
⋅=−
+
⋅−
−
= −
−
+
−
=−
G
G
(b) In unit vector notation
3
ˆ
ˆ
4
3
12
12( 5.14i 6.13 j) ( 7.72i 9.20 j) 12(94.6k) 1.14 10 k
AB AB
×=
×
+
×
−
−
=
=
×
GG
(c) We note that the azimuthal angle is undefined for a vector along the
z
axis.
Thus, our
result is “1.14
×
10
3
,
θ
not defined, and
φ
= 0
°
.”
(d) Since
A
→
is in the
xy
plane, and
A
B
×
G
G
is perpendicular to that plane, then the answer is
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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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