If `l_1,""""m_1,""""n_1` and `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 these are `m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1` .

Explanation

As, `l_1,""""m_1,""""n_1`
and `l_2,""""m_2,""""n_2`
are the direction cosines of two mutually
perpendicular lines

So,the line is cross product of lines having directional cosines `l_1,""""m_1,""""n_1`
and `l_2,""""m_2,""""n_2`

Required line=`[[i,j,k],[l_1,m_1,n_1],[l_2,m_2,n_2]]`

=`(m_1n_2-m_2n_1)i+(l_2n_1-l_1n_2)j+(l_1m_2-l_2m_1)k)`

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