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a. Show that the following are vector equations for the same line: L₁:7= (-1,0, 4) + s(−1, 2, 5), sɛR, and L₂:7=(4,-10, -21) + m(-2, 4, 10), m=R b. Show that the following are vector equations for different lines: L3:7 = (1, 6, 1) + (−1, 1, 2), IER, and +4 ( 121/1/2-1). KER L4:7= (-3, 10, 12) + k

a. Show that the following are vector equations for the same line: L₁:7= (-1,0, 4) + s(−1, 2, 5), sɛR, and L₂:7=(4,-10, -21) + m(-2, 4, 10), m=R b. Show that the following are vector equations for different lines: L3:7 = (1, 6, 1) + (−1, 1, 2), IER, and +4 ( 121/1/2-1). KER L4:7= (-3, 10, 12) + k

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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1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(-2, 4, -1). Since a vector equation of a line can be written in many ways, it is useful to be able to tell if different forms are actually equivalent. 2. a. Show that the following are vector equations for the same line: L₁:7=(-1,0, 4) + s(-1, 2, 5), sER, and L₂:7 (4, -10, -21) + m(-2, 4, 10), m=R = b. Show that the following are vector equations for different lines: L3:7 = (1, 6, 1) + (−1, 1, 2), lɛR, and 1 1 L4:7 = (−3, 10, 12) + k( ½, —⁄, −1 ), ker 2' 2'
Transcribed Image Text:1. Determine the vector and parametric equations of the line passing through P(-2, 3, 5) and Q(-2, 4, -1). Since a vector equation of a line can be written in many ways, it is useful to be able to tell if different forms are actually equivalent. 2. a. Show that the following are vector equations for the same line: L₁:7=(-1,0, 4) + s(-1, 2, 5), sER, and L₂:7 (4, -10, -21) + m(-2, 4, 10), m=R = b. Show that the following are vector equations for different lines: L3:7 = (1, 6, 1) + (−1, 1, 2), lɛR, and 1 1 L4:7 = (−3, 10, 12) + k( ½, —⁄, −1 ), ker 2' 2'
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