Let $L _ { 1 }$ and $L _ { 2 }$ be the following straight lines. $$L _ { 1 } : \frac { x - 1 } { 1 } = \frac { y } { - 1 } = \frac { z - 1 } { 3 } \text { and } L _ { 2 } : \frac { x - 1 } { - 3 } = \frac { y } { - 1 } = \frac { z - 1 } { 1 } .$$ Suppose the straight line $$L : \frac { x - \alpha } { l } = \frac { y - 1 } { m } = \frac { z - \gamma } { - 2 }$$ lies in the plane containing $L _ { 1 }$ and $L _ { 2 }$, and passes through the point of intersection of $L _ { 1 }$ and $L _ { 2 }$. If the line $L$ bisects the acute angle between the lines $L _ { 1 }$ and $L _ { 2 }$, then which of the following statements is/are TRUE? (A) $\alpha - \gamma = 3$ (B) $l + m = 2$ (C) $\alpha - \gamma = 1$ (D) $l + m = 0$
Let $L _ { 1 }$ and $L _ { 2 }$ be the following straight lines.
$$L _ { 1 } : \frac { x - 1 } { 1 } = \frac { y } { - 1 } = \frac { z - 1 } { 3 } \text { and } L _ { 2 } : \frac { x - 1 } { - 3 } = \frac { y } { - 1 } = \frac { z - 1 } { 1 } .$$
Suppose the straight line
$$L : \frac { x - \alpha } { l } = \frac { y - 1 } { m } = \frac { z - \gamma } { - 2 }$$
lies in the plane containing $L _ { 1 }$ and $L _ { 2 }$, and passes through the point of intersection of $L _ { 1 }$ and $L _ { 2 }$. If the line $L$ bisects the acute angle between the lines $L _ { 1 }$ and $L _ { 2 }$, then which of the following statements is/are TRUE?\\
(A) $\alpha - \gamma = 3$\\
(B) $l + m = 2$\\
(C) $\alpha - \gamma = 1$\\
(D) $l + m = 0$