Consider in (x, y, z) space the vector field V(x, y,z) = (2x + 3y, 2y + 3x, –4z) and thefunctionF(x,y,z) = a · x² + b•y² + c•z² +d •x • y, (x,y,z) E R³.a) Find constants a, b,c and d so that V = VF .b) Compute the tangential line integral of V along the right half of the unit circle inthe (y, z) plane centered at (0,1,1) with an orientation of your choice.

Given : vector field Vx, y, z=2x+3y, 2y+3x, -4z and the function Fx, y,…

Consider in (x, y, z) space the vector field V(x, y,z) = function (2x + 3y, 2y + 3x, –4z) and the %3D F(x,y,z) = a · x² + b·y² + c • z² + d • x • y, (x,y,z) E R³. a) Find constants a, b,c and d so that V = VF . %3D b) Compute the tangential line integral of V along the right half of the unit circle in the (y, z) plane centered at (0,1,1) with an orientation of your choice.

Consider in (x, y, z) space the vector field V(x, y,z) = function (2x + 3y, 2y + 3x, –4z) and the %3D F(x,y,z) = a · x² + b·y² + c • z² + d • x • y, (x,y,z) E R³. a) Find constants a, b,c and d so that V = VF . %3D b) Compute the tangential line integral of V along the right half of the unit circle in the (y, z) plane centered at (0,1,1) with an orientation of your choice.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.2: Inner Product Spaces

Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...

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