Question

Determine which statements are true in reals3. (Selectall that apply.)

(a)Two lines parallel to a third line are parallel.
(b) Twolines perpendicular to a third line are parallel.
(c) Twoplanes parallel to a third plane are parallel.
(d) Twoplanes perpendicular to a third plane are parallel.
(e) Twolines parallel to a plane are parallel.
(f) Twolines perpendicular to a plane are parallel.
(g) Twoplanes parallel to a line are parallel.
(h) Twoplanes perpendicular to a line are parallel.
(i) Twoplanes either intersect or are parallel.
(j) Twolines either intersect or are parallel.
(k) A plane and a line either intersector are parallel.

Answer 1

(a)Two lines parallel to a third line are parallel.

(c) Two planes parallel to a third plane are parallel.

(f) Two lines perpendicular to a plane are parallel.

(h) Two planes perpendicular to a line are parallel.

(i) Two planes either intersect or are parallel.

(k) A plane and a line either intersect or are parallel

Explanation:

(b) Two lines perpendicular to a third line are parallel. -- No. The y-, and z-axes are perpendicular to the x-axis, but are not parallel.

(d) Two planes perpendicular to a third plane are parallel. -- No. The x-y and y-z coordinate planes are both perpendicular to the x-z coordinate plane, but are at right angles to each other.

(e) Two lines parallel to a plane are parallel. -- No. Two intersecting lines in the plane z=0 are both parallel to the plane z=1, but are not parallel to each other.

(g) Two planes parallel to a line are parallel. -- No. Both the x-z plane and the y-z plane are parallel to the line (x, y, z) = (1, 1, z), but those coordinate planes are perpendicular to each other.

(j) Two lines either intersect or are parallel. -- No. The lines may be skew, running different directions in parallel panes.