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19 February, 19:48

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.

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  1. 19 February, 22:30
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    (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

    Step-by-step 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.
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