how to find projection of conical surface lying along z axis on the xy plane ?????????????

- anonymous

how to find projection of conical surface lying along z axis on the xy plane ?????????????

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- jtvatsim

Think of shining a light down the z axis. If you have a cone, and shine a light on the very top, what kind of shadow will it cast? A circle. So the projection of a conical surface lying along the z axis is a circle on the xy plane (assuming you mean that the tip of the cone is on the z axis).

- anonymous

|dw:1360306137675:dw|

- jtvatsim

Yep, that will be a circle shadow :)

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## More answers

- anonymous

i m okk.with circle but want to know that if |dw:1360306291929:dw|

- anonymous

|dw:1360306412506:dw|

- anonymous

@jtvatsim help plss

- anonymous

@hartnn help..........

- jtvatsim

wow... not sure on that part... sorry :( anyone else got ideas?

- anonymous

basically i m working on conversion of cartesian to spherical coordinates????????????

- anonymous

@saifoo.khan help plss

- anonymous

@Ashleyisakitty help plss...........

- anonymous

any idea @Ashleyisakitty

- anonymous

@jim_thompson5910 ,@Luis_Rivera ......pls help any1

- anonymous

@rebeccaskell94 help

- anonymous

I'm sorry, what is the dot product of?

- anonymous

|dw:1360307330028:dw|

- anonymous

I can't understand what it says do you mind typing it out?

- anonymous

THETA is a constant and represents equation of cone in spherical coordinates

- anonymous

Are you asking for the projection of theta onto the x axis? There is no straightforward solution. in spherical polar, the conversion is x = (rho)*cos(theta)sin(phi). however, the fact that you have a unit vector for theta is confusing. The two are independent of each other. It's like comparing apples and oranges.

- anonymous

For a "normal cone" the equation is typically theta = pi/4 if that helps

- anonymous

plsss...........w8 i m clearing what i intended to ask @khoala4pham

- anonymous

|dw:1360307890501:dw|

- anonymous

|dw:1360308115075:dw|

- anonymous

while finding A(thetha) i m getting |dw:1360308301921:dw|

- anonymous

@robtobey help

- anonymous

Please use the equations. I have no idea what these symbols mean. If your question is what is the unit vector of theta dotted with that of x, then I have no idea. The conversion of x to theta or vice versa involves a Jacobian which is computationally tedious. They are of different coordinate systems!! The mapping of x,y,z to r,theta,phi is not straightforward. It's not simply asking what i dot j is or what j dot k is.
Honestly, you are asking for help but what is the question asking? The projection of a cone onto the xy plane is any number of circles. They are inherently level curves of the cone.

- anonymous

see i m asking if we have to convert cartesian to spherical coordinates we need to find the A(theta) FR THATwe need projection of cone first over over the xy plane ..then its projection along x and y axis to get dot product with unit vector along x and y axis respectively.

- anonymous

see the case of finding A(r) it is simple the projection of line with distance r from origin on xy plane frst........that is |dw:1360308936766:dw|

- anonymous

@Hero plsssssssssssssssssssss answer

- anonymous

I don't even know what you are getting at. if you are looking for the conversion of cartesian to spherica;,
x= rho*sin(phi)*cos(theta)
y = rho*sin(phi)*sin(theta)
z = rho*cos(phi)
But the rest of your information is extremely lacking. This is some random cone in random space that can be projected in ANY way imaginable. If my light source is sufficiently far away, your projection is huge; if it's close, miniscule. There is no way to pinpoint one. You HAVE to specify at least a level curve or SOME CHARACTERISTIC of the cone. The equation theta = 1, theta = 2, theta = 3 are all cones.
You are overcomplicating this problem if I am to understand correctly. Project it onto x and then onto y and take the vector sum. But you can't use spherical and cartesian at the same time! It's like calculating velocity in miles per hour and getting distance in kilometers without converting...it doesn't work.

- anonymous

but in my book answers are :|dw:1360309534965:dw|.................anyway thanks fr d help

- anonymous

I'd dare say that is incorrect. for the first unit vector, by virtue of being a unit vector, it has to be <1,0,0>, <0,1,0>, <0,0,1>. Ax and Ay (if this is your notation) is <1,0,0> and <0,1,0>. One of those two dot products MUST equal zero.

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