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$If the line \frac{x - 2}{- 1} = \frac{y + 2}{1} = \frac{z + k}{4} is one of the angle bisectors of the lines \frac{x}{1} = \frac{y}{- 2} = \frac{z}{3} and \frac{x}{- 2} = \frac{y}{3} = \frac{z}{1} then$
$the value of k is$

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detailed solution

Correct option is D

Since point of intersection of the given lines is (0, 0, 0), it must lie on the angle bisector. so, 0−2−1=0+21=0+k4⇒ k=8 See the angle between the angular bisectors and the given line must be same

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If the line x−2−1=y+21=z+k4 is one of the angle bisectors of the lines x1=y−2=z3 and x−2=y3=z1 then the value of k is

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$If the line \frac{x - 2}{- 1} = \frac{y + 2}{1} = \frac{z + k}{4} is one of the angle bisectors of the lines \frac{x}{1} = \frac{y}{- 2} = \frac{z}{3} and \frac{x}{- 2} = \frac{y}{3} = \frac{z}{1} then$
$the value of k is$