Does anyone know where I can find the derivation of the cross product. I know how to use it and the like but I do not understand why the norm of the matrix :
\left[ \begin{array}{ccc}i & j & k \\n1 & n2 & n3 \\m1 & m2 & m3 \\\end{array}\right]
yields the vector perpendicular to 'n' and 'm'.
I need a little help with this problem. Its from the 2004 physics bowl.
50. A solid spherical conducting shell has inner radius a and outer radius 2a. At the center of the shell is located a point charge +Q. What must the excess charge on the shell be in order for the charge density on the...
Hey all. I was reading that story about the physics student who is asked to show whether hell is endothermic or exothermic (here's the http://www.people.virginia.edu/~rjh9u/hellthrm.html to the story) when I came upon the following statements:
1. If hell is expanding at a slower rate than...
Is anyone familiar with the derivation for this formula for torsion.
\tau = \frac {\left( \begin{array}{ccc} \dot{x} & \ddot{x} & \dddot{x}\\\dot{y}& \ddot{y}& \ddot{y} \\\dot{z} & \ddot{z} & \dddot{z}\end{array} \right)} {|v \times a|^2}
I know of expressing torsion as [tex] \tau =...
I see how I can use induction to find why 1-\frac{1}{(n+1)(n!)}
gives the sum of the series but how would you analytically come up with that expression in the first place. My calculator did it in a second, how did it generate the expression. Is there something I am missing?
I’ve been playing around with the infinite series:
\sum_{k=1}^\infty \frac{k}{(k+1)!}
I haven’t really gotten anywhere with it however I punched it into my calculator and it determined the sum to be 1. And the sum of n terms of the series equals
1-\frac{1}{(n+1)(n!)}
Why is this so...