Question

Will award medal. and fan
let r= and g(x,y,z)=-1/sqrt(x^2+y^2+z^2) (x,y,z)does not=0 show that (upside down delta)g=vector r/|r|^3

Answer 1

@ganeshie8

Answer 2

\[\nabla g = \langle g_x, ~g_y, ~g_z \rangle \]

Answer 3

how do i even start. i found what the gradient vector needs to be equal to

Answer 4

Find the paritials and observe that
\[\|\vec{r}\| = \sqrt{x^2+y^2+z^2}\]

Answer 5

isnt ||r||cubed as well?

Answer 6

so g_x=x/(x^2+y^2+z^2)^3/2

Answer 7

Yes which is same as x/||r||^3