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This implies that Eq. (2.26) is sensitive to the direction of the angle . Thus, if b is rotated counter-
clockwise from a , sin is positive. But if b is rotated clockwise from a , sin is negative.
A simple example demonstrates the angular sensitivity of Eq. (2.26).
With reference to Fig. 2.34: let
a
=
i
b
=
i
+
j
a =
j
Therefore,
a ·
b
j
·
i
+
j
sin
=
=
2 =
2
1
a
b
1
·
a
θ
a
b
Figure 2.35.
In contrast, with reference to Fig. 2.35,
a
=
i
b
=
i
j
a =
j
Therefore,
j
·
i
j
1
2
sin
=
· 2 =−
1
 
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