Let S be the surface defined by p(x, y, z) = 0 where z = f(x,y); i.e. z is a function of the variables x and y. (i) Let P be an arbitrary point on S with position vector p. Show that the equation of the tangent plane to the surface S at p is given by Vo(x-p) = 0 where x = xi+yj+zk is the position vector of an arbitrary point in R³. Hint: Start with the usual equation of the tangent plane at the point P = (a, b, f(a, b)) on the surface z = f(x, y): : - f(a, b) = = af -(a, b) (x − a) + ?x af ду -(a, b) (y — b)
Let S be the surface defined by p(x, y, z) = 0 where z = f(x,y); i.e. z is a function of the variables x and y. (i) Let P be an arbitrary point on S with position vector p. Show that the equation of the tangent plane to the surface S at p is given by Vo(x-p) = 0 where x = xi+yj+zk is the position vector of an arbitrary point in R³. Hint: Start with the usual equation of the tangent plane at the point P = (a, b, f(a, b)) on the surface z = f(x, y): : - f(a, b) = = af -(a, b) (x − a) + ?x af ду -(a, b) (y — b)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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