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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

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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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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