GIVEN: The surface given by : x² + y² + 2z² = 6 and the line L: c(t) = (1 −t, 2+t, 1 +2t), t = R FIND: The set of points: Ln9. (Be careful: The form of the answer must be a set! & Remember your answer must be boxed)
GIVEN: The surface given by : x² + y² + 2z² = 6 and the line L: c(t) = (1 −t, 2+t, 1 +2t), t = R FIND: The set of points: Ln9. (Be careful: The form of the answer must be a set! & Remember your answer must be boxed)
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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Question
Please please For the first image attached please do the calculations similar to the second image attached
![[10] (2) GIVEN: The surface given by : x² + y² + 2z² = 6
and the line L: c(t) = (1-t, 2+t, 1+2t), t = R
FIND: The set of points: LnQ.
(Be careful: The form of the answer must be a set!
& Remember your answer must be boxed)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9755e55f-b204-4ec5-8a10-7bbad16cf793%2Fb0d39ea0-ad16-4df3-b74c-cb4915709bd7%2Fbl9wu38_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] (2) GIVEN: The surface given by : x² + y² + 2z² = 6
and the line L: c(t) = (1-t, 2+t, 1+2t), t = R
FIND: The set of points: LnQ.
(Be careful: The form of the answer must be a set!
& Remember your answer must be boxed)
![[10] (2) GIVEN: The surface given by : x² - y² + 2z² = 9
and the line L: c(t) = (1-t, 2+t, 1 + 2t), t = R
FIND: The set of points: LnQ.
(Be careful: The form of the answer must be a set!
& Remember your answer must be boxed)
METHOD: PELAN OP = c(t), t€ R
and ΡΕΩ
↔ −(1-t)²- (2+t)² + 2 (1 + 2t)² = 9
⇒ −(1-2t + t²) - (4 + 4t + t²)
II I
+ 2 (1 + 4 t + 4t² ) = 9
6t² + 6t -3 = 9
⇒
2t² + 2t -1 = 3
2t² + 2t -4 = 0
You must use
LOGIC.
t²+t-2=0
⇒ (t-1)(t + 2) = 0 ↔ ±=-2 ort=1
t=-2 : OP = Ĉ(-2) = (3, 0,− 3)
t= 1: OP= Ĉ (1) = (0, 3, 3)
Hence,
LNN = {(3,0,-3), (0,3,3)}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9755e55f-b204-4ec5-8a10-7bbad16cf793%2Fb0d39ea0-ad16-4df3-b74c-cb4915709bd7%2Fkp2feps_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] (2) GIVEN: The surface given by : x² - y² + 2z² = 9
and the line L: c(t) = (1-t, 2+t, 1 + 2t), t = R
FIND: The set of points: LnQ.
(Be careful: The form of the answer must be a set!
& Remember your answer must be boxed)
METHOD: PELAN OP = c(t), t€ R
and ΡΕΩ
↔ −(1-t)²- (2+t)² + 2 (1 + 2t)² = 9
⇒ −(1-2t + t²) - (4 + 4t + t²)
II I
+ 2 (1 + 4 t + 4t² ) = 9
6t² + 6t -3 = 9
⇒
2t² + 2t -1 = 3
2t² + 2t -4 = 0
You must use
LOGIC.
t²+t-2=0
⇒ (t-1)(t + 2) = 0 ↔ ±=-2 ort=1
t=-2 : OP = Ĉ(-2) = (3, 0,− 3)
t= 1: OP= Ĉ (1) = (0, 3, 3)
Hence,
LNN = {(3,0,-3), (0,3,3)}
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