Consider the lines $\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$ and $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$ the equation of the line which:
Bisects the angle between the lines is $\frac{x}{3} = \frac{y}{3} = \frac{z}{6}$
Bisects the angle between the lines is $\frac{x}{1} = \frac{y}{2} = \frac{z}{3}$
Passes through origin and is perpendicular to the given lines is $x = y = -z$
None of these
Step-by-Step Solution
Key Concept: The bisector of two lines has direction ratios equal to the sum and difference of their respective direction cosines.
If two lines have direction cosines $l_1, m_1, n_1$ and $l_2, m_2, n_2$, the direction ratio of their bisectors can be found using the property that bisectors divide the angle equally. The direction ratios of the bisectors are proportional to $l_1 \pm l_2$, $m_1 \pm m_2$, and $n_1 \pm n_2$.
Correct Answer: I need to find the angle bisectors of the two given lines and check which option is correct.
**Given lines:**
- Line 1: $\frac{x}{2} = \frac{y}{3} = \frac{z}{5}$ with direction ratios $(2, 3, 5)$
- Line 2: $