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Mathematics
Problem
If
l
1
,
m
1
,
n
1
l_1, m_1, n_1
l
1
,
m
1
,
n
1
and
l
2
,
m
2
,
n
2
l_2, m_2, n_2
l
2
,
m
2
,
n
2
are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of them are
m
1
n
2
−
m
2
n
1
m_1 n_2 - m_2 n_1
m
1
n
2
−
m
2
n
1
;
n
1
l
2
−
n
2
l
1
n_1 l_2 - n_2 l_1
n
1
l
2
−
n
2
l
1
;
l
1
m
2
−
l
2
m
1
l_1 m_2 - l_2 m_1
l
1
m
2
−
l
2
m
1
.
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