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C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R) (u²+ 4u + 3)i + (u² + 6)j + (u + 2) k (u € R)

C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R) (u²+ 4u + 3)i + (u² + 6)j + (u + 2) k (u € R)

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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(b) Let C₁, C₂2 and C3 be the curves in R³ with parametrisations C₁: r₁(s) (s − 2)i + (2s² − 1)j + k (SER) C₂ r₂(t) 2t² i + (3t+7)j + (t+1) k (t = R) C3 r3(u) (u² + 4u+3)i + (u² + 6)j + (u + 2)k (u ¤R) = = = respectively. (i) Show that C₁, C₂ and C3 intersect at the point (0, 7, 1). answer. (ii) Find the tangent vectors to the curves C₁, C₂ and C3 at the point (0, 7, 1). Do these tangent vectors lie in a common plane in R³? Justify your (iii) Is it possible to find a surface z = h(x, y) for which the curves C₁, C₂ and C3 all lie on this surface? Justify your answer.
Transcribed Image Text:(b) Let C₁, C₂2 and C3 be the curves in R³ with parametrisations C₁: r₁(s) (s − 2)i + (2s² − 1)j + k (SER) C₂ r₂(t) 2t² i + (3t+7)j + (t+1) k (t = R) C3 r3(u) (u² + 4u+3)i + (u² + 6)j + (u + 2)k (u ¤R) = = = respectively. (i) Show that C₁, C₂ and C3 intersect at the point (0, 7, 1). answer. (ii) Find the tangent vectors to the curves C₁, C₂ and C3 at the point (0, 7, 1). Do these tangent vectors lie in a common plane in R³? Justify your (iii) Is it possible to find a surface z = h(x, y) for which the curves C₁, C₂ and C3 all lie on this surface? Justify your answer.
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