If l(1), m(1), n(1) and l(2),m(2),n(2) a...

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_(1)n_(2)-m_(2)n_(1),n_(1)l_(2)-n_(2)l_(1),l_(1)m_(2)-l_(2)m_(1)`.

`1_(1)1_(2), m _(1) m_(2), n _(1) n _(2)`

`m_(1) n_(2) -m_(2) n_(1), n _(1) 1_(2) -n_(2) 1_(1), 1_(1)m_(2)-1_(2) m _(1)`

`(1_(1))/(1_(2)), (m_(1))/(m_(2)), (n_(1))/(n_(2))`

`m _(1) n_(2) +m_(2) n_(1), n _(1) 1_(2) + n_(2) 1_(1),1_(1)m_(2) + 1_(2) m_(1)`

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