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Mathematics
Problem
For vectors
a
=
(
a
1
,
a
2
,
a
3
)
\mathbf a=(a_1,a_2,a_3)
a
=
(
a
1
,
a
2
,
a
3
)
and
b
=
(
b
1
,
b
2
,
b
3
)
\mathbf b=(b_1,b_2,b_3)
b
=
(
b
1
,
b
2
,
b
3
)
, the coefficient of
j
^
\hat{j}
j
^
in
a
×
b
\mathbf a\times\mathbf b
a
×
b
is a)
a
1
b
3
−
a
3
b
1
a_1 b_3 - a_3 b_1
a
1
b
3
−
a
3
b
1
b)
a
1
b
2
−
a
2
b
1
a_1 b_2 - a_2 b_1
a
1
b
2
−
a
2
b
1
c)
a
3
b
1
−
a
1
b
3
a_3 b_1 - a_1 b_3
a
3
b
1
−
a
1
b
3
d)
a
3
b
1
+
a
1
b
3
a_3 b_1 + a_1 b_3
a
3
b
1
+
a
1
b
3
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