(a) Explanation Given: The function is x y − z = 0 . Formula used: Equation of tangent plane at point ( x 0 , y 0 , z 0 ) is given by, F x ( x 0 , y 0 , z 0 ) ( x − x 0 ) + F y ( x 0 , y 0 , z 0 ) ( y − y 0 ) + F z ( x 0 , y 0 , z 0 ) ( z − z 0 ) = 0 Calculation: x y − z = 0 . Let partial differentiate the function with respect to z , F z ( x , y , z ) = − 1 Let partial differentiate the function with respect to y , F y ( x , y , z ) = x Let us partial differentiate the function with respect to x , F x ( x , y , z ) = y At point ( − 2 , − 3 , 6 ) , The partial derivatives are F x ( − 2 , − 3 , (b) To determine F x ( − 2 , − 3 , 6 ) = − 3 , F y ( − 2 , − 3 , 6 ) = − 2 , F z ( − 2 , − 3 , 6 ) = − 1 Is given, find set of symmetric equation for the normal line to the surface at ( − 2 , − 3 , 6 )

10th Edition

ISBN: 9781285948133

Author: Ron Larson; Bruce H. Edwards

Publisher: Cengage Learning US

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Chapter 13.7, Problem 26E

(a)

To determine

To calculate: The function is xy−z=0.

Is given, find equation of the tangent plane to the surface at (−2,−3,6)

(b)

To determine

Fx(−2,−3,6)=−3, Fy(−2,−3,6)=−2, Fz(−2,−3,6)=−1

Is given, find set of symmetric equation for the normal line to the surface at (−2,−3,6)

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Chapter 13.7, Problem 25E

Chapter 13.7, Problem 23E

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The function is x y − z = 0 . Is given, find equation of the tangent plane to the surface at ( − 2 , − 3 , 6 )

Solution Summary: The author explains that the function is xy-z=0. The equation of the tangent plane to the surface at 3x+2y+z =-6 is given.

Videos

To calculate: The function is xy−z=0.

Is given, find equation of the tangent plane to the surface at (−2,−3,6)

Fx(−2,−3,6)=−3, Fy(−2,−3,6)=−2, Fz(−2,−3,6)=−1

Is given, find set of symmetric equation for the normal line to the surface at (−2,−3,6)

Want to see the full answer?

Chapter 13 Solutions

The function is x y − z = 0 . Is given, find equation of the tangent plane to the surface at ( − 2 , − 3 , 6 )

Solution Summary: The author explains that the function is xy-z=0. The equation of the tangent plane to the surface at 3x+2y+z =-6 is given.

Videos

To calculate: The function is xy−z=0. Is given, find equation of the tangent plane to the surface at (−2,−3,6)

Fx(−2,−3,6)=−3, Fy(−2,−3,6)=−2, Fz(−2,−3,6)=−1 Is given, find set of symmetric equation for the normal line to the surface at (−2,−3,6)

Want to see the full answer?

Chapter 13 Solutions

To calculate: The function is xy−z=0.

Is given, find equation of the tangent plane to the surface at (−2,−3,6)

Fx(−2,−3,6)=−3, Fy(−2,−3,6)=−2, Fz(−2,−3,6)=−1

Is given, find set of symmetric equation for the normal line to the surface at (−2,−3,6)