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Consider the surface What is the equation of the tangent plane to the surface at the point P(3,-3,-4)? O-4x - 5y-3z = 15 3x3y4z = 15 3x-3y-4z=0 0-2x³ O-4x - 5y-3z=0 -2x³ - 2xy + 2xyz = 36. What is the equation of the line normal to the surface at the point P(3,-3,-4)? 3 ·0-0)- (1) O = -3 O 2xy + 2xyz = 0 O -24 -0-0) = t -30 4 O +t -18, 3 -0-0-0 -3 + t -24 -30 -18, 3 -0-0 = t -3 4 -24 -0-0-0) +t -18, -24 -18 3 -3 4

Consider the surface What is the equation of the tangent plane to the surface at the point P(3,-3,-4)? O-4x - 5y-3z = 15 3x3y4z = 15 3x-3y-4z=0 0-2x³ O-4x - 5y-3z=0 -2x³ - 2xy + 2xyz = 36. What is the equation of the line normal to the surface at the point P(3,-3,-4)? 3 ·0-0)- (1) O = -3 O 2xy + 2xyz = 0 O -24 -0-0) = t -30 4 O +t -18, 3 -0-0-0 -3 + t -24 -30 -18, 3 -0-0 = t -3 4 -24 -0-0-0) +t -18, -24 -18 3 -3 4

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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Consider the surface What is the equation of the tangent plane to the surface at the point P(3,-3,-4)? -4x - 5y3z = 15 3x3y4z = 15 3x - 3y4z = 0 -2x³ - 2xy + 2xyz = 0 -4x - 5y-3z = 0 What is the equation of the line normal to the surface at the point P(3,-3,-4)? 3 -0-0-0 = -3 + t -4 O -2x3 - 2xy + 2xyz = 36. -0-6 = t -30 O O O -24 -18 3 -0-0-0) 8 -3 +t 4 -18 -24 3 ·0-C-C (²) = -30 + t -3 -18, 3 -0-0) = t -3 -4 -24 -18, -24
Transcribed Image Text:Consider the surface What is the equation of the tangent plane to the surface at the point P(3,-3,-4)? -4x - 5y3z = 15 3x3y4z = 15 3x - 3y4z = 0 -2x³ - 2xy + 2xyz = 0 -4x - 5y-3z = 0 What is the equation of the line normal to the surface at the point P(3,-3,-4)? 3 -0-0-0 = -3 + t -4 O -2x3 - 2xy + 2xyz = 36. -0-6 = t -30 O O O -24 -18 3 -0-0-0) 8 -3 +t 4 -18 -24 3 ·0-C-C (²) = -30 + t -3 -18, 3 -0-0) = t -3 -4 -24 -18, -24
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