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Mathematics
Problem
Prove that the three lines from
O
O
O
with direction cosines
l
1
,
m
1
,
n
1
l_1, m_1, n_1
l
1
,
m
1
,
n
1
;
l
2
,
m
2
,
n
2
l_2, m_2, n_2
l
2
,
m
2
,
n
2
and
l
3
,
m
3
,
n
3
l_3, m_3, n_3
l
3
,
m
3
,
n
3
are coplanar, if
l
1
(
m
2
n
3
−
n
2
m
3
)
+
m
1
(
n
2
l
3
−
l
2
n
3
)
+
n
1
(
l
2
m
3
−
l
3
m
2
)
=
0
l_1(m_2n_3 - n_2m_3) + m_1(n_2l_3 - l_2n_3) + n_1(l_2m_3 - l_3m_2) = 0
l
1
(
m
2
n
3
−
n
2
m
3
)
+
m
1
(
n
2
l
3
−
l
2
n
3
)
+
n
1
(
l
2
m
3
−
l
3
m
2
)
=
0
.
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