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

`l_1,m_1,n_1`and `l_2,m_2,n_2`are the direction cosines

Hence,

`l_1l_2+m_1m_2+n_1n_2=0`

`l_1^2+m_1^2+n_1^2=1`

`l_2^2+m_2^2+n_2^2=1`


Let l,m,n be the direction cosines of the line, hence,

`ll_1+mm_1+nn_1=0`

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