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l₁ : (x, y, z) = (23, 98, -36) +r(8, 32, -12) where r ER and l₂ : (x, y, z) = (–9, −30, 12) + t2, 8, −3) where t = R. Show that the lines ₁ and ₂ are identical.

l₁ : (x, y, z) = (23, 98, -36) +r(8, 32, -12) where r ER and l₂ : (x, y, z) = (–9, −30, 12) + t2, 8, −3) where t = R. Show that the lines ₁ and ₂ are identical.

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Let l₁: (x, y, z) = (23, 98, -36)+7(8, 32, -12) where r ER and l₂: (x, y, z) = (-9, -30, 12) + (2,8, -3) where t = R. Show that the lines ₁ and ₂ are identical. Solution Identify the required vectors Let P₁ be the support point of the line ₁. Let vi be the generator vector of the line l₁. Let P₂ be the support point of the line 12. Let 2 be the generator vector of the line l₂. We know P₁ V₁ P₂ = (23,98,-36) (let r = 0 and write the components of the point) (8,32,-12) (-9,-30,12) (let t = 0 and write the components of the point) V₂ = (2,8,-3) and P₂P₁ = (write the components of the vector P2P₁)
Transcribed Image Text:Let l₁: (x, y, z) = (23, 98, -36)+7(8, 32, -12) where r ER and l₂: (x, y, z) = (-9, -30, 12) + (2,8, -3) where t = R. Show that the lines ₁ and ₂ are identical. Solution Identify the required vectors Let P₁ be the support point of the line ₁. Let vi be the generator vector of the line l₁. Let P₂ be the support point of the line 12. Let 2 be the generator vector of the line l₂. We know P₁ V₁ P₂ = (23,98,-36) (let r = 0 and write the components of the point) (8,32,-12) (-9,-30,12) (let t = 0 and write the components of the point) V₂ = (2,8,-3) and P₂P₁ = (write the components of the vector P2P₁)
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