# Vector Algebra

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• Feb 18th 2010, 02:06 AM
Chris0724
Vector Algebra
Given

V (x , y , z) = 10xyz - (x^2)z + 10y(z^2) -20

find the grad of V.

if i transfer to the form below the how do i associate the -20 with ?

10xyz ax - (x^2)z ay + 10y(z^2) az -20

anyone able to help?
is the answer 10yz - 0 + 20yz ?

many thanks (Happy)
• Feb 18th 2010, 02:43 AM
elliotician
Please explain how you got this form '10xyz ax - (x^2)z ay + 10y(z^2) az -20'?
and how you get 10yz +20yz

If you are trying to get the gradient of V(x,y,z) you will need to express the gradient in the direction of x, the direction of y and the direction of z.

Thus you should be looking at how you might express this gradient as a vector with partial derivatives.
• Feb 18th 2010, 04:57 AM
HallsofIvy
Quote:

Originally Posted by Chris0724
Given

V (x , y , z) = 10xyz - (x^2)z + 10y(z^2) -20

find the grad of V.

if i transfer to the form below the how do i associate the -20 with ?

10xyz ax - (x^2)z ay + 10y(z^2) az -20

anyone able to help?
is the answer 10yz - 0 + 20yz ?

many thanks (Happy)

The derivative of a constant is 0.

However, your whole concept here is wrong. The grad of a function is a vector:
$\nabla f(x,y,z)= \frac{\partial f}{\partial x}\vec{i}+ \frac{\partial f}{\partial y}\vec{j}+ \frac{\partial f}{\partial z}\vec{k}$
not another real valued function as you have written it.