Section 12.5: Lines & Planes

Determine whether each statement is true or false in \(\mathbb{R}^3\). (a) Two lines parallel to a third line are parallel. (b) Two lines perpendicular to a third line are parallel. (c) Two planes parallel to a third plane are parallel. (d) Two planes perpendicular to a third plane are parallel. (e) Two lines parallel to a plane are parallel. (f) Two lines perpendicular to a plane are parallel. (g) Two planes parallel to a line are parallel. Two planes perpendicular to a line are parallel. (i) Two planes either intersect or are parallel. (j) Two lines either intersect or are parallel. (k) A plane and a line either intersect or are parallel.