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A triangle ABC has coordinates of the po...

A triangle ABC has coordinates of the points A, B,C as (1, 2, 3), (2, 3, 1) and (-1, 4, 7) respectively.If internal angle bisector of angle A meets the side BC at D, then the direction cosines of AD are `l,m,n`. Th value of `9 l^2 + 8 m^2 - 4 n^2` equals

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