First slide

Straight lines in 3D

Question

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

Moderate

A

1
B

2
C

4
D

8

Solution

Since point of intersection of the given lines is (0, 0, 0), it must lie on the angle bisector.
$so, \frac{0 - 2}{- 1} = \frac{0 + 2}{1} = \frac{0 + k}{4}$
$\Rightarrow k = 8$

See the angle between the angular bisectors and the given line must be same

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