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If `l_(1), m_(1), n_(1), l_(2), m_(2), n_(2), l_(3), m_(3), n_(3)` be the direction cosines of three mutually perpendicular straight lines, then show that the straight line whose direction numbers are `(l_(1) + l_(2) + l_(3)), (m_(1)+m_(2)+m_(3)), (n_(1)+n_(2)+n_(3))` makes equal angles with the given lines.

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