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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
Related questions
Question
![(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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38e693cf-3870-4eab-9920-bd211e6a8ee6%2F9c074136-2103-4296-bf6c-c62c434c756b%2F4efxi2e_processed.jpeg&w=3840&q=75)
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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