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puchie1225
14.12.2021 •
Mathematics
Could some one help me understand
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Ответ:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
All segments skew to SW: WX, ST
All segments skew to UT: UY, TX
Step-by-step explanation:
Let's begin by explaining the following:
Two line segments are parallel only if their slopes are identical, allowing them to never intersect.
Hence, according to this definition we have:
Segments parallel to XT: YU, ZV, WS
Segments parallel to ZY: VU, WX
Segments parallel to ZS: None
Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.
Hence, according to this definition we have:
Plane parallel to plane STU: WXY
Plane parallel to plane UVZ: TSW
Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.
Hence, according to this definition we have:
All segments skew to SW: WX, ST
WZ and SV do not match the condition, since they are in the same plane where SW is,
All segments skew to UT: UY, TX
UV and ST do not match the condition, since they are in the same plane where UT is.