Question

planes x and y intersect at a right - angle. (overrightarrow{ab}) and (overrightarrow{cg}) lie in plane x and do not intersect. (overrightarrow{rs}) lies in plane y. which statements are true? select three options. (square) (overrightarrow{ab}) and (overrightarrow{cg}) are parallel. (square) (overrightarrow{ab}) and (overrightarrow{rs}) are parallel. (square) (overrightarrow{cg}) and (overrightarrow{rs}) are perpendicular. (square) (overrightarrow{ab}) and (overrightarrow{rs}) must intersect. (square) (overrightarrow{cg}) lies in plane x. (square) (overrightarrow{rs}) lies in plane x.

Explanation:

Step1: Recall parallel - line definition

Parallel lines in a plane are lines that do not intersect. Since $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ lie in plane $X$ and do not intersect, they are parallel.

Step2: Analyze perpendicular - line and plane relationship

Planes $X$ and $Y$ intersect at a right - angle. $\overleftrightarrow{RS}$ lies in plane $Y$ and $\overleftrightarrow{CG}$ lies in plane $X$. So $\overleftrightarrow{CG}$ and $\overleftrightarrow{RS}$ are perpendicular.

Step3: Check line - plane membership

It is given that $\overleftrightarrow{CG}$ lies in plane $X$.

Answer:

$\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ are parallel; $\overleftrightarrow{CG}$ and $\overleftrightarrow{RS}$ are perpendicular; $\overleftrightarrow{CG}$ lies in plane $X$