If $l_1, m_1, n_1 \: and \: l_2, m_2, n_2$ are direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are $m_1n_2-m_2n_1, n_1l_2-n_2l_1, l_1m_2-l_2m_1.$

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