Question
amining Lines in Three Dimensions Are the lines in the diagram perpendicular parallel skew, or none of these? land m square land n square m and n square
Answer
4.3
(211 Votes)
Blake
Veteran · Tutor for 11 years
Answer
To determine the relationship between the lines in the diagram, we will consider each pair of lines separately based on the provided picture details.1. Lines
and
:Since line
is perpendicular to plane A and line
is perpendicular to plane B, and planes A and B intersect along line
, we cannot immediately conclude the relationship between lines
and
without additional information. If planes A and B are perpendicular to each other, then lines
and
would be parallel, as they would both be perpendicular to the line of intersection of the planes (line
). However, if planes A and B are not perpendicular, lines
and
could be skew lines. Since we do not have information about the angle between planes A and B, we cannot definitively determine the relationship between lines
and
.Answer: The relationship between lines
and
cannot be determined with the given information.2. Lines
and
:Line
is perpendicular to plane B, and line
lies in plane B. Therefore, line
is perpendicular to line
because a line perpendicular to a plane is also perpendicular to every line in that plane that it intersects.Answer: Lines
and
are perpendicular.3. Lines
and
:Line
lies in plane A, and line
is the intersection line between planes A and B. Since line
is perpendicular to plane A, it is also perpendicular to any line in plane A that it intersects. However, we do not have information that line
intersects line
. If line
intersects line
, then they would be perpendicular. If line
does not intersect line
, then they could be skew lines. Without additional information, we cannot determine the relationship between lines
and
.Answer: The relationship between lines
and
cannot be determined with the given information.