Need some help understanding unit vector equation please!

[Jrolyan]

Hi, I haven't been able to find anywhere that can help me with the question I've linked below so any help I can get here is greatly appreciated!

https://gyazo.com/f8a87e4261def6dc813a1a2b98e8ef5f

So far I have tried just deriving 5xy with respect to x and so on to get an answer of (5y+z+x) but this is wrong and the site I am using doesn't give any feedback.



There is also another question here that is a bit different that I'm also struggling with if I can get a 2nd opinion on that too. I don't know how to apply partial derivatives to the dot product.

https://gyazo.com/d1750ceb8739aaaf3d625984eae7a648

For this one I thought that the cross product of two unit vectors was 1, so I interpreted the first one as the dot product of 1 and 2 which would just be 2 but I don't think that is right. As for the other two I don't know where to start.

Thank you!

 

[HallsofIvy]

Hi, I haven't been able to find anywhere that can help me with the question I've linked below so any help I can get here is greatly appreciated!

https://gyazo.com/f8a87e4261def6dc813a1a2b98e8ef5f

So far I have tried just deriving 5xy with respect to x and so on to get an answer of (5y+z+x) but this is wrong and the site I am using doesn't give any feedback.

"Deriving with respect to x and y"? You seem to have your uploads in reversed order!
In your second upload you have
\(\displaystyle \nabla\cdot <5xy, yz, xz>= \frac{\partial 5xy}{\partial x}+ \frac{\partial yz}{\partial y}+ \frac{\partial xz}{\partial z}= 5y+ z+ x\) so what you have is correct.

There is also another question here that is a bit different that I'm also struggling with if I can get a 2nd opinion on that too. I don't know how to apply partial derivatives to the dot product.

https://gyazo.com/d1750ceb8739aaaf3d625984eae7a648

"Partial derivatives"? There is nothing about differentiating anything in this problem!

For this one I thought that the cross product of two unit vectors was 1, so I interpreted the first one as the dot product of 1 and 2 which would just be 2 but I don't think that is right. As for the other two I don't know where to start.

You need to review cross and dot product! The cross product of two vectors is not a number at all, it is a vector. And "the dot product of 1 and 2" makes no sense- you can only take the dot product of two vectors.

Thank you!