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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

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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

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

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BlakeVeteran · 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 \(l\) and \(m\):Since line \(m\) is perpendicular to plane A and line \(l\) is perpendicular to plane B, and planes A and B intersect along line \(n\), we cannot immediately conclude the relationship between lines \(l\) and \(m\) without additional information. If planes A and B are perpendicular to each other, then lines \(l\) and \(m\) would be parallel, as they would both be perpendicular to the line of intersection of the planes (line \(n\)). However, if planes A and B are not perpendicular, lines \(l\) and \(m\) 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 \(l\) and \(m\).Answer: The relationship between lines \(l\) and \(m\) cannot be determined with the given information.2. Lines \(l\) and \(n\):Line \(l\) is perpendicular to plane B, and line \(n\) lies in plane B. Therefore, line \(l\) is perpendicular to line \(n\) because a line perpendicular to a plane is also perpendicular to every line in that plane that it intersects.Answer: Lines \(l\) and \(n\) are perpendicular.3. Lines \(m\) and \(n\):Line \(m\) lies in plane A, and line \(n\) is the intersection line between planes A and B. Since line \(m\) 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 \(m\) intersects line \(n\). If line \(m\) intersects line \(n\), then they would be perpendicular. If line \(m\) does not intersect line \(n\), then they could be skew lines. Without additional information, we cannot determine the relationship between lines \(m\) and \(n\).Answer: The relationship between lines \(m\) and \(n\) cannot be determined with the given information.
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