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$A = (- 1, 2, - 3), B = (5, 0, - 6), C = (0, 4, - 1)$ . If $l, m, n$ be the direction cosines of the internal angular bisector of $∠ B A C$ , then $l - m - n =$

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a

28714

b

22714

c

38714

d

12714

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detailed solution

Correct option is D

The vector along the internal angular bisector of a¯,b¯ isa¯a±b¯bHerea¯=AB¯ and b¯=AC¯It implies that a¯=6i−2j−3k and b¯=i+2j+2kHence, the vector along the internal angular bisector of ∠BAC is a¯a+b¯b=25i+8j+5k21Therefore, the direction cosines are25714,8714,5714It implies that l−m−n=12714

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$P (0, 4, - 1), Q (- 1, 2, - 3) and R (5, 0, - 6)$ are the vertices of a triangle. The direction ratios of the internal angular bisector of $∠ P Q R$ are

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