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(a) The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the (1, 1, 1). Hence, find the equation of the plane = point A with position vector a tangent to S at A.

(a) The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the (1, 1, 1). Hence, find the equation of the plane = point A with position vector a tangent to S at A.

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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(a) The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the (1, 1, 1). Hence, find the equation of the plane point A with position vector a tangent to S at A. (b) The curve C is defined by the section of surface S on the (x, y)-plane with x ≥ 0. Sketch C and evaluate the line integral LOVA where ds is an element of arc length. I = √4-x+3y² ds
Transcribed Image Text:(a) The surface S is defined by x + y² + z³ = 3. Find a vector normal to S at the (1, 1, 1). Hence, find the equation of the plane point A with position vector a tangent to S at A. (b) The curve C is defined by the section of surface S on the (x, y)-plane with x ≥ 0. Sketch C and evaluate the line integral LOVA where ds is an element of arc length. I = √4-x+3y² ds
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