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ˆ
cossin
ˆ
sincossincoscos
ˆ
cossinsinsincos
ˆ
:vectorsUnit
R
R
R
r
2
2
222
2
2
22
2
2
2
2
2
22
2
2
sin
1
)(sin
sin
11
)
sin
1
(
sin
1
)(sin
sin
1
sin
sin
1
)(
sin
1
)(sin
sin
1
)(
1
)(
sin
1
)sin(
sin
1
)sin(
sin
1
sin
1
ˆ
1
ˆˆ
sin
1
ˆ
1
ˆˆ
(1.9.16) - (1.9.12) Using
+
+
=
+
+
=
+
+
=
+
+
=
+
+
=
+
+
=
f
R
f
RR
f
R
RR
f
R
f
RR
f
R
RR
f
u
R
u
R
uR
RR
Ru
R
uR
R
uR
RR
f
R
f
RR
f
f
RRR
R
R
R
R
u
eee
eee
z
1-18. Continued
θ
φR
e
ee
e
eeu
ˆ
)(
1
ˆ
)(
1
sin
1
ˆ
)(sin
sin
1
ˆ
)()[(
1
ˆ
)]sin()([
sin
1
ˆ
)]()sin([
sin
1
2
−
+
−
+
−
=
−
+
−
+
−
=
R
R
R
RR
u
Ru
RR
Ru
RR
u
R
u
u
R
uRu
RR
uR
R
u
R
RuuR
R
