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(c) Using results in part (b), show that the minimum distance is |(ba). (d₁ × d₂)| ||d₁ x d₂|| M = (d) Using results in part (c), determine the minimum distance between the skew lines r₁ = (-1,2,0) + λ(2, 1, 3), r₂ = (0, 5, -1) + µ(1, 2, 3), λμ Ε.

(c) Using results in part (b), show that the minimum distance is |(ba). (d₁ × d₂)| ||d₁ x d₂|| M = (d) Using results in part (c), determine the minimum distance between the skew lines r₁ = (-1,2,0) + λ(2, 1, 3), r₂ = (0, 5, -1) + µ(1, 2, 3), λμ Ε.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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need help with c) and d)

2. Two lines in R³ are said to be skew if they are neither parallel nor intersecting. In this question, we will determine the minimum distance between two skew lines. (a) If the lines r₁ = a + 2₁, λμ ER, are skew lines, explain why the minimum distance between these two lines must be in the direction n = = d₁ × d₂. r₂ b + µd₂, for some scalar values k, î, îâî. (b) By denoting the position vectors that minimise the distance between the skew lines in part (a) as p₁ on ₁ and ₂ on r₂, show that - kn = P₂ - P₁ = b - a + d₂ - Âd₁, M = (c) Using results in part (b), show that the minimum distance is |(b − a) · (d₁ × d₂)| ||d₁ × d₂|| (d) Using results in part (c), determine the minimum distance between the skew lines r₁ = (−1, 2, 0) + λ(2, 1, 3), r₂ = (0,5, -1) + µ(1, 2, 3), λ,μ Ε R.
Transcribed Image Text:2. Two lines in R³ are said to be skew if they are neither parallel nor intersecting. In this question, we will determine the minimum distance between two skew lines. (a) If the lines r₁ = a + 2₁, λμ ER, are skew lines, explain why the minimum distance between these two lines must be in the direction n = = d₁ × d₂. r₂ b + µd₂, for some scalar values k, î, îâî. (b) By denoting the position vectors that minimise the distance between the skew lines in part (a) as p₁ on ₁ and ₂ on r₂, show that - kn = P₂ - P₁ = b - a + d₂ - Âd₁, M = (c) Using results in part (b), show that the minimum distance is |(b − a) · (d₁ × d₂)| ||d₁ × d₂|| (d) Using results in part (c), determine the minimum distance between the skew lines r₁ = (−1, 2, 0) + λ(2, 1, 3), r₂ = (0,5, -1) + µ(1, 2, 3), λ,μ Ε R.
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