Explanation Given: The equation of surfaces is z = x 2 + y 2 and z = 4 − y . Formula used: Cross product of the two gradients ∇ F ( x , y , z ) and ∇ G ( a , b , c ) is, ∇ F ( a , b , c ) × ∇ G ( x , y , z ) = | i j k a b c x y z | = ( b z − c y ) i − ( a z − c x ) j + ( a y − b x ) k Calculation: z = x 2 + y 2 . F ( x , y , z ) = z − x 2 − y 2 Let us partial differentiate F ( x , y , z ) with respect to z . F z ( x , y , z ) = 1 Let us partial differentiate F ( x , y , z ) with respect to y . F y ( x , y , z ) = − 2 y Let us partial differentiate F ( x , y , z ) with respect to x . F x ( x , y , z ) = − 2 x gradient ∇ F ( x , y , z ) = − 2 x i − 2 y j + k Put x = 2 , y = − 1 , z = 5 to get, ∇ F ( 2 , − 1 , 5 ) = − 4 i + 2 j + k z = 4 − y . G ( x , y , z ) = z + y − 4 Let us partial differentiate G ( x , y , z ) with respect to y

11th Edition

ISBN: 9781337275347

Author: Ron Larson, Bruce H. Edwards

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 13.7, Problem 28E

To determine

To calculate: The equation of surfaces is z=x2+y2 and z=4−y, is given, find parametric equation for the tangent line to the given curve of intersection of the surfaces at point (2,−1,5) where z=x2+y2 and z=4−y.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 13.7, Problem 27E

Chapter 13.7, Problem 29E

Students have asked these similar questions

Sketch the curve represented by the parametric equations (indicate the orientation of the curve), and write the corresponding rectangular equation by eliminating the parameter x-2, y-t ++ -1 0.5 05 05- -05- 0.5 + --05

Help4

plz provide accurate solution

Chapter 13 Solutions

Calculus (MindTap Course List)

Ch. 13.1 - Think About It Explain why z2=x+3y is not a...Ch. 13.1 - Prob. 2E Ch. 13.1 - Determine whether graph is a function. Use the...Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Determining Whether an Equation Is a Function In...Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The equation of surfaces is z = x 2 + y 2 and z = 4 − y , is given, find parametric equation for the tangent line to the given curve of intersection of the surfaces at point ( 2 , − 1 , 5 ) where z = x 2 + y 2 and z = 4 − y .

Solution Summary: The author explains that the equation of surfaces is z=x2+y 2. Then, find parametric equation for the tangent line to the given curve of intersection of the

Videos

To calculate: The equation of surfaces is z=x2+y2 and z=4−y, is given, find parametric equation for the tangent line to the given curve of intersection of the surfaces at point (2,−1,5) where z=x2+y2 and z=4−y.

Want to see the full answer?

Chapter 13 Solutions