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If "l"1,("\ m")1,("\ n")1("\ and\ l")2,(...

If `"l"_1,("\ m")_1,("\ n")_1("\ and\ l")_2,("\ m")_2,"n"_2` be 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),"\ "("n"_1"l"_2-"n"_2"l"_1),"\ "("l"_1"m"_2-"l"_2"m"_1)dot`

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