Cross Product in 3D Cylindrical or Spherical coordinates
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When i take a cross product of two vectors (Cylinder base in x,y plane) for example d(phi)cross d(z), how do i know if the resultant Vector protrudes out of the page or goes inside? I know the right hand rule but in terms of Cylinder and Spheres its hard to implement. This might be a very basic question but non the less it is very important for the Integrals of Surfaces.
I would be very thankful to know if you have any tips or tricks to understand the normal vectors in 3 dimensions.
integration vectors surfaces cross-product
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
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add a comment |
$begingroup$
When i take a cross product of two vectors (Cylinder base in x,y plane) for example d(phi)cross d(z), how do i know if the resultant Vector protrudes out of the page or goes inside? I know the right hand rule but in terms of Cylinder and Spheres its hard to implement. This might be a very basic question but non the less it is very important for the Integrals of Surfaces.
I would be very thankful to know if you have any tips or tricks to understand the normal vectors in 3 dimensions.
integration vectors surfaces cross-product
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
$endgroup$
$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52
add a comment |
$begingroup$
When i take a cross product of two vectors (Cylinder base in x,y plane) for example d(phi)cross d(z), how do i know if the resultant Vector protrudes out of the page or goes inside? I know the right hand rule but in terms of Cylinder and Spheres its hard to implement. This might be a very basic question but non the less it is very important for the Integrals of Surfaces.
I would be very thankful to know if you have any tips or tricks to understand the normal vectors in 3 dimensions.
integration vectors surfaces cross-product
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
$endgroup$
When i take a cross product of two vectors (Cylinder base in x,y plane) for example d(phi)cross d(z), how do i know if the resultant Vector protrudes out of the page or goes inside? I know the right hand rule but in terms of Cylinder and Spheres its hard to implement. This might be a very basic question but non the less it is very important for the Integrals of Surfaces.
I would be very thankful to know if you have any tips or tricks to understand the normal vectors in 3 dimensions.
integration vectors surfaces cross-product
integration vectors surfaces cross-product
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
asked Dec 11 '18 at 11:13
Sherlock HomiesSherlock Homies
18513
18513
$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52
add a comment |
$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52
$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52
$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52
add a comment |
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$begingroup$
If you have two vectors in cylindrical coordinates with components $(r_1 , varphi_1 , z_1)$ and $(r_2 , varphi_2 , z_2)$, their cross product has $z$ component $r_1 r_2 sin(varphi_2 - varphi_1)$. In spherical coordinates, how is the "page plane" defined?
$endgroup$
– Nominal Animal
Dec 12 '18 at 20:52