Showing a vector field is imcompressible

question dude
Messages
80
Reaction score
0

Homework Statement


attachment.php?attachmentid=455997&d=1440616258.jpg


Homework Equations

The Attempt at a Solution



As you can see, the solution is shown just below the question.

Essentially, I don't understand how the x, y and z component of the vector field has been separated because the numerator of the vector field's fraction is: (x^2 + y^2 + z^2)^(1/2)

It seems like they've just taken x^2 out and square rooted it to get 'x', but you can't do that, can you?
 
Physics news on Phys.org
question dude said:

Homework Statement


attachment.php?attachmentid=455997&d=1440616258.jpg


Homework Equations

The Attempt at a Solution



As you can see, the solution is shown just below the question.

Essentially, I don't understand how the x, y and z component of the vector field has been separated because the numerator of the vector field's fraction is: (x^2 + y^2 + z^2)^(1/2)

It seems like they've just taken x^2 out and square rooted it to get 'x', but you can't do that, can you?

That isn't what they have done. The numerator is bold faced ##\bf{r}## and the denominator is ##r##. The first is the vector and the second its magnitude. r = xi + yj + zk.
 
LCKurtz said:
That isn't what they have done. The numerator is bold faced ##\bf{r}## and the denominator is ##r##. The first is the vector and the second its magnitude. r = xi + yj + zk.

Do I treat the non-bold r as a constant?

If sub in bold r, I get:

G = [(x^2 + y^2 + z^2)^0.5 ] / 4*pi*r^3
 
question dude said:
Do I treat the non-bold r as a constant?

If sub in bold r, I get:

G = [(x^2 + y^2 + z^2)^0.5 ] / 4*pi*r^3

I just noticed in your graphic under (b) they have ##{\bf r} = \sqrt{x^2+y^2+z^2}## That should not have been a bold face r. The bold face r represents the vector and the plain r its magnitude, which is not constant.
 
Thread 'Use greedy vertex coloring algorithm to prove the upper bound of χ'
Hi! I am struggling with the exercise I mentioned under "Homework statement". The exercise is about a specific "greedy vertex coloring algorithm". One definition (which matches what my book uses) can be found here: https://people.cs.uchicago.edu/~laci/HANDOUTS/greedycoloring.pdf Here is also a screenshot of the relevant parts of the linked PDF, i.e. the def. of the algorithm: Sadly I don't have much to show as far as a solution attempt goes, as I am stuck on how to proceed. I thought...

Similar threads

Back
Top