Determine which statements are true in R^3. (Select all that apply.) (a) Two lin

Question

Determine which statements are true in R^3. (Select all that apply.) (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. (h) 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.

Explanation / Answer

Solution:

(a) True

Two lines parallel to a third llne are parallel.

Let line L1||L3 and L2||L3 then L1||L2

(b) True

Two lines perpendicular to a third line are parallel.

direction of two lines which are perpendicular to third will be same there therefore they are parallel

(c) Ture

Two planes parallel to a third plane are parallel and it is always true

(d) True

Two planes perpendicular to a third plane are parallel and it is always true

(e) False

Two lines parallel to a plane may or may not be parallel parallel.

(f) Ture

Two lines perpendicular to plane parallel and always true

(g) True

Two planes are parallel to a line are parallel and always true

(h) True

Two planes are perpendicular to a line are parallel.

(i) True

Two planes are either intersect or are parallel

(j) Ture

Two lines are either intersect or are parallel

(k) True

a plane or a line either intersect or parallel

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