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Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). In Exercises 65 and 66, deter- mine whether the lines, 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. 65. L1: x = 3 + 2t, y = -1 + 4t, z = 2 – t; -0

Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). In Exercises 65 and 66, deter- mine whether the lines, 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. 65. L1: x = 3 + 2t, y = -1 + 4t, z = 2 – t; -0

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). In Exercises 65 and 66, deter- mine whether the lines, 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. 65. L1: x = 3 + 2t, y = -1 + 4t, z = 2 – t; -0 <t < L2: x = 1 + 4s, y = 1 + 2s, z = -3 + 4s; L3: x = 3 + 2r, y = 2 + r, z = -2 + 2r; -00 <s < ∞ -00 < r < ∞ 66. L1: x = 1 + 2t, y = -1 – t, z = 3t; -00 <t< ∞ I| L2: x = 2 – s, y = 3s, z = 1 + s; -00 < s< ∞ %3D L3: x = 5 + 2r, y = 1 – r, z = 8 + 3r; -∞< r < ∞
Transcribed Image Text:Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). In Exercises 65 and 66, deter- mine whether the lines, 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. 65. L1: x = 3 + 2t, y = -1 + 4t, z = 2 – t; -0 <t < L2: x = 1 + 4s, y = 1 + 2s, z = -3 + 4s; L3: x = 3 + 2r, y = 2 + r, z = -2 + 2r; -00 <s < ∞ -00 < r < ∞ 66. L1: x = 1 + 2t, y = -1 – t, z = 3t; -00 <t< ∞ I| L2: x = 2 – s, y = 3s, z = 1 + s; -00 < s< ∞ %3D L3: x = 5 + 2r, y = 1 – r, z = 8 + 3r; -∞< r < ∞
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