[10] (1) z²+yz + 2, and the point P₁ = (1,– 1,1). Note that P. = Q. GIVEN: The surface : xy + 2xz+z = FIND: The equation of the tangent plane, σ, to so that the point P, is the point of tangency. EXPRESS your answer in the form: O: ax+by+cz = d
[10] (1) z²+yz + 2, and the point P₁ = (1,– 1,1). Note that P. = Q. GIVEN: The surface : xy + 2xz+z = FIND: The equation of the tangent plane, σ, to so that the point P, is the point of tangency. EXPRESS your answer in the form: O: ax+by+cz = d
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
![[10] (1) GIVEN: The surface Q: 2xy + yz² = 7+2xz+z²,
and the point P₁ = (1, 2, 3). Note that P₁ = Q.
FIND: The equation of the tangent plane, o, to
so that the point Po is the point of tangency.
EXPRESS your answer in the form: o: ax+by+ cz = d
METHOD:
Q: 2xy + yz² = 7+2xz+z²
2zJ-2zz +yz² − z² = 7
DEFINE F: R³ R₂
3
F(x, y, z) = 2xy − 2xz+yz²_z²
▼F = (²y-2z, 2x+z²,−2x+2yz−2z)
⇒ VF(1,2,3) = (-2,11,4)
Hence,
O: −2(x-1)+11(7-2) + 4(z-3) = 0
O: 2x +11y + 4z = 32](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F767da4a8-c644-4919-9393-25d8fa6c982f%2F9f6846ee-a4c8-4ded-9ebe-8b4440939b30%2Firxflyl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] (1) GIVEN: The surface Q: 2xy + yz² = 7+2xz+z²,
and the point P₁ = (1, 2, 3). Note that P₁ = Q.
FIND: The equation of the tangent plane, o, to
so that the point Po is the point of tangency.
EXPRESS your answer in the form: o: ax+by+ cz = d
METHOD:
Q: 2xy + yz² = 7+2xz+z²
2zJ-2zz +yz² − z² = 7
DEFINE F: R³ R₂
3
F(x, y, z) = 2xy − 2xz+yz²_z²
▼F = (²y-2z, 2x+z²,−2x+2yz−2z)
⇒ VF(1,2,3) = (-2,11,4)
Hence,
O: −2(x-1)+11(7-2) + 4(z-3) = 0
O: 2x +11y + 4z = 32
![[10] (1)
GIVEN: The surface : xy + 2xz+z
and the point Po= (1,
-
z² + y2 + 2,
1,1). Note that Po € Q
=
FIND: The equation of the tangent plane, o, to
so that the point Po is the point of tangency.
EXPRESS your answer in the form: O: ax+by+cz = d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F767da4a8-c644-4919-9393-25d8fa6c982f%2F9f6846ee-a4c8-4ded-9ebe-8b4440939b30%2F6cx1gs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[10] (1)
GIVEN: The surface : xy + 2xz+z
and the point Po= (1,
-
z² + y2 + 2,
1,1). Note that Po € Q
=
FIND: The equation of the tangent plane, o, to
so that the point Po is the point of tangency.
EXPRESS your answer in the form: O: ax+by+cz = d
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