Understanding Positive Orientation of Point C: A Guide

[etf]

Here is my task and my attempt of solution:

How to use fact that C is positively orientated viewed from point (10,0,0)? I'm not sure I understand it.

 

[LCKurtz]

It would be much more convenient for us if you would type your question and work on this site instead of posting un-editable images and which require us to open another window.

 

[LCKurtz]

How to use fact that C is positively orientated viewed from point (10,0,0)? I'm not sure I understand it.

Me neither. Perhaps it meant (0,0,10). I would just work it going either direction for $\theta$ and see what happens.

 

[SammyS]

Here is my task and my attempt of solution:

View attachment 65981

How to use fact that C is positively orientated viewed from point (10,0,0)? I'm not sure I understand it.

Here is the image:

Is C supposed to be a closed path ?

 

[LCKurtz]

Is C supposed to be a closed path ?

It's closed alright. Here's a picture of it:

 

[SammyS]

It's closed alright. Here's a picture of it:
...

Yes the intersection makes a complete loop, but if the instruction is correct regarding the view from (10, 0, 0), then only part of that path is oriented in a positive direction.

That's why I asked (the OP) if the path is supposed to be closed. If so then the point (10, 0, 0) is incorrect as you have suggested.

 

[etf]

It would be much more convenient for us if you would type your question and work on this site instead of posting un-editable images and which require us to open another window.

I didn't learn latex yet so that's reason why I'm posting images. I could write my equations here but I thought it would be much easier for you to follow if I "draw" it using MathType software.

It's (10,0,0) point, I didn't make mistake... I'm still uncertain about solving this problem...
I forgot to write, result is pi.

 

[LCKurtz]

I didn't learn latex yet so that's reason why I'm posting images. I could write my equations here but I thought it would be much easier for you to follow if I "draw" it using MathType software.

It isn't.

It's (10,0,0) point, I didn't make mistake... I'm still uncertain about solving this problem...
I forgot to write, result is pi.

I think you had best ask your Teacher to clarify. It makes sense to talk about clockwise or counterclockwise orientation if you look down at it along the $z$ axis, but not from out the $x$ axis. And I don't see any interpretation of the problem that gives $\pi$ for the answer. Are you sure you copied the integral itself correctly?

 

[etf]

I copied it correctly. I will ask teacher for help.
Thanks anyway!

 

[LCKurtz]

I copied it correctly. I will ask teacher for help.
Thanks anyway!

I would be interested to know what your teacher tells you.

 

[etf]

I will inform you as soon as he explain me.

 

[etf]

Here are few examples with similar statement:

1.Find $$\int\limits_C{} {{y^2}dx + xdy + zdz}$$ where C is curve formed by intersection of $${x^2} + {y^2} = x + y$$ and $$2({x^2} + {y^2}) = z$$ orientated positively viewed from point (0,0,2R). (Result 0)

2.Find $$\int\limits_C {(y - z)dx + (z - x)dy + (x - y)} dz\\$$ where C is curve formed by intersection of $${x^2} + {y^2} = {a^2}$$ and $$\frac{x}{a} + \frac{z}{h} = 1$$ (a greather than 0, h greather than 0), passed in positive direction viewed from point (2a,0,0). (Result -2*pi*a*(a+h))