a) Find the point(s) on the surface S : a2 – y² + 6z = 0, where the normal line to the surface S is parallel to the line passing through P(3, –1,0) and Q(5, 3, 6). And also write the tangent plane equation to the surface S at that point. 1 b) Does f(x, y, z) = x² + y? – 2² increase or decrease at the point P(3, – 1,0) in the direction of the vector J = (1,1, v2)? Explain! %3D

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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a) Find the point (s) on the surface S : x2 – y? + 6z = 0,
where the normal line to the surface S is parallel to the
line passing through P(3, –1,0) and Q(5, 3, 6). And
also write the tangent plane equation to the surface S
at that point.
1
b) Does f(x, y, 2) = x² +y? – 2² increase or decrease
at the point P(3,–1,0) in the direction of the vector
ū = (1,1, v2)? Explain!
Transcribed Image Text:a) Find the point (s) on the surface S : x2 – y? + 6z = 0, where the normal line to the surface S is parallel to the line passing through P(3, –1,0) and Q(5, 3, 6). And also write the tangent plane equation to the surface S at that point. 1 b) Does f(x, y, 2) = x² +y? – 2² increase or decrease at the point P(3,–1,0) in the direction of the vector ū = (1,1, v2)? Explain!
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