Apr 12, 2013 · It looks like [itex]\hat{z}[/itex] is a unit vector in the axial direction, [itex]\hat{\phi}[/itex] is a unit vector in the circumferential direction, [itex]\hat{R}[/itex] is a unit vector pointing from the origin in an arbitrary spatial direction, and [itex]\theta[/itex] is the angle between the unit vector [itex]\hat{R}[/itex] and the z axis.

Feb 27, 2014 · It's not clear why you are trying to calculate cross products in non-cartesian coordinate systems. AFAIK, the vector cross product is defined only for cartesian coordinates, and then only for 3-dimensional (and 7-dimensional) coordinates.

Mar 22, 2004 · f(x,y) = sin(y) hold x constant and we get f(c,y) = sin(y) So the cross-section (the yz plane) at location c is the sine function. Then we note that the constant c is arbitrary and has no effect on the cross section, so every cross section we get by holding x constant will be the sine function. So what we have is the union of all lines parallel ...

Feb 28, 2009 · A pile of Earth standing on flat ground near an abandoned mine has height 13 meters. The ground is the xy-plane; the origin is directly below the top of the pile and the z-axis is upward. The cross-section at height z is given by [tex]x^2 + y^2 = 13 - z[/tex] for [tex]0 \leq z \leq 13[/tex] with x, y, and z in meters.

Jun 20, 2011 · Why are i, j, and k perfered in many texts to represent the 3 spatial dimensions instead of (what seems to me to be more intuitive) x, y, and z? Insights Blog -- Browse All Articles -- Physics Articles Physics Tutorials Physics Guides Physics FAQ Math Articles Math Tutorials Math Guides Math FAQ Education Articles Education Guides Bio/Chem ...

May 4, 2008 · Point the 4 fingers in the direction of u (the first vector in the cross product). Keeping those fingers pointing along u, rotate or twist your hand so that the palm faces clockwise (i.e., towards the direction of v, the 2nd vector in the product). Your thumb is now pointing in the direction of u x v.

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Jul 25, 2012 · Homework Statement Homework Equations The Attempt at a Solution So this isn't a specific question, I'm just having trouble with my definitions. In my book for f(x) = (x - 2) ((x + 1)^2) (x-4) it says that the zeros are at x = 2, -1, 4. On the page it …

Oct 26, 2008 · So I need ALL the functions f s.t. f(x+y) = f(x) + f(y) for all integers x,y. Clearly any linear function f will do this, and these are all isomorphisms. Also f(x) = 0 for all x satisfies the definition of the homomorphism. This is not injective, surjective, nor an …

May 22, 2013 · There are many equivalent ways to define the cross product. One of them is $$(a_1,a_2,a_3)\times(b_1,b_2,b ...