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Mathematics
Mathematics
Problem
Let
r
^
\hat{\mathbf{r}}
r
^
be a unit vector satisfying
r
^
×
a
=
b
\hat{\mathbf{r}} \times \mathbf{a} = \mathbf{b}
r
^
×
a
=
b
, where
∣
a
∣
=
3
|\mathbf{a}| = \sqrt{3}
∣
a
∣
=
3
and
∣
b
∣
=
2
|\mathbf{b}| = \sqrt{2}
∣
b
∣
=
2
. Then, a.
r
^
=
2
3
(
a
+
a
×
b
)
\hat{\mathbf{r}} = \frac{2}{3}(\mathbf{a} + \mathbf{a} \times \mathbf{b})
r
^
=
3
2
(
a
+
a
×
b
)
b.
r
^
=
1
3
(
a
+
a
×
b
)
\hat{\mathbf{r}} = \frac{1}{3}(\mathbf{a} + \mathbf{a} \times \mathbf{b})
r
^
=
3
1
(
a
+
a
×
b
)
c.
r
^
=
2
3
(
−
a
+
a
×
b
)
\hat{\mathbf{r}} = \frac{2}{3}(-\mathbf{a} + \mathbf{a} \times \mathbf{b})
r
^
=
3
2
(
−
a
+
a
×
b
)
d.
r
^
=
1
3
(
−
a
+
a
×
b
)
\hat{\mathbf{r}} = \frac{1}{3}(-\mathbf{a} + \mathbf{a} \times \mathbf{b})
r
^
=
3
1
(
−
a
+
a
×
b
)
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