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. (overrightarrow{ab}) and (overrightarrow{cg}) are parallel. (overrightarrow{ab}) and (overrightarrow{rs}) are parallel. (overrightarrow{cg}) and (overrightarrow{rs}) are perpendicular. (overrightarrow{ab}) and (overrightarrow{rs}) must intersect. (overrightarrow{cg}) lies in plane x. (overrightarrow{rs}) lies in plane x.

Explanation:

Step1: Analyze parallel - lines in plane

Lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ lie in plane $X$ and do not intersect. In a plane, non - intersecting lines are parallel. So $\overleftrightarrow{AB}$ and $\overleftrightarrow{CG}$ are parallel.

Step2: Analyze perpendicular - lines between planes

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

Step3: Analyze line - plane relationship

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 $X$