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Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. L1: L2: L3: x= -2-t, y=-2-2t, z=1-2t, -∞

Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. L1: L2: L3: x= -2-t, y=-2-2t, z=1-2t, -∞

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. L1: x= -2-t, y=-2-2t, z=1-2t, -∞0<t<∞ L2: x = -6-2s, y=-7-4s, z=2-4s, -∞0<$<∞0 x = −4+2r, y = -5+ 3r, z=2-r. -∞<r<∞ L3: xxx Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) A. L1 and L2 are parallel. Their distance is √26 O B. L1 and L2 are skew. Their distance is OC. L1 and L2 intersect at the point (..) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) OA. L1 and L3 are parallel. Their distance is B. L1 and L3 are skew. Their distance is C. L1 and L3 intersect at the point (-2-2.1) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) A. L2 and L3 are skew. Their distance is O B. L2 and L3 intersect at the point (D OC. L2 and L3 are parallel. Their distance is
Transcribed Image Text:Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines. L1: x= -2-t, y=-2-2t, z=1-2t, -∞0<t<∞ L2: x = -6-2s, y=-7-4s, z=2-4s, -∞0<$<∞0 x = −4+2r, y = -5+ 3r, z=2-r. -∞<r<∞ L3: xxx Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) A. L1 and L2 are parallel. Their distance is √26 O B. L1 and L2 are skew. Their distance is OC. L1 and L2 intersect at the point (..) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) OA. L1 and L3 are parallel. Their distance is B. L1 and L3 are skew. Their distance is C. L1 and L3 intersect at the point (-2-2.1) Select the correct choice below and fill in the answer box(es) to complete your choice. (Type exact answers, using radicals as needed.) A. L2 and L3 are skew. Their distance is O B. L2 and L3 intersect at the point (D OC. L2 and L3 are parallel. Their distance is
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