. In each of the following, you are given two objects in 3-space. First, determine whether the given objects intersect. Then, for those that do intersect, find the point(s) or curve of intersection. (a) x + y+ z = 2 and х — Зу — 2 — 12 (b) ři(t) = (2t + 1)i+ (6 +2t) j + (4t – 4) k and T2(t) = (5 – t)ỉ+ tj+ (4 – 2t) k (с) х — t+1, у — 4— 21, z3 21 + 1 and x = t, y = t, z = 3t – 2
. In each of the following, you are given two objects in 3-space. First, determine whether the given objects intersect. Then, for those that do intersect, find the point(s) or curve of intersection. (a) x + y+ z = 2 and х — Зу — 2 — 12 (b) ři(t) = (2t + 1)i+ (6 +2t) j + (4t – 4) k and T2(t) = (5 – t)ỉ+ tj+ (4 – 2t) k (с) х — t+1, у — 4— 21, z3 21 + 1 and x = t, y = t, z = 3t – 2
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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Transcribed Image Text:6. In each of the following, you are given two objects in 3-space. First, determine whether the given objects
intersect. Then, for those that do intersect, find the point (s) or curve of intersection.
(a) x + y+z = 2 and
х — Зу — х 3D 12
(b) ri(t) = (2t +1)i+ (6+ 2t) j + (4t – 4) k and 2(t) = (5 – t) i+tj+ (4 – 21) k
(c) x =t+1, y= 4 – 2t, z = 2t +1 and
x = t, y = t, z = 3t – 2
(d) r +y+2z = 6 and F(t) = (1+ 6t) i+ j + (1 – 3t) k
(е) х +у — 2х — 6
and
x = 1+t, y = 2t, z = 1 – t
(f) x – y+ z = 3
and
-2x + 2y – 2z = 4
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