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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