2. For the following pair of equations, determine if they represent the same, parallel, or different lines Show r your work L1: r (1, 0, 3) + s(3, -6, 3) and L2: (2, -2, 5) + t(2, -4, 2)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
2. For the following pair of equations, determine if they represent the same, parallel, or different lines Show
r
your work L1: r
(1, 0, 3) + s(3, -6, 3) and L2:
(2, -2, 5) + t(2, -4, 2)
Transcribed Image Text:2. For the following pair of equations, determine if they represent the same, parallel, or different lines Show r your work L1: r (1, 0, 3) + s(3, -6, 3) and L2: (2, -2, 5) + t(2, -4, 2)
Expert Solution
Step 1

The equation of the first line L1 is r=1, 0, 3+s3, -6, 3 and the second line

L2 is r=2, -2, 5+t2, -4, 2.

We can rewrite as

L1: x=1+3s, y=-6s, z=3+3sL2: x=2+2t, y=-2-4t, z=5+2t

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