a) V(r/r^n)=1(r/r^n) - n(rr/r^(n+2)) b) V (dot) (r/r^n) = (3-n)/r^n c) V x (r/r^

Question

                                a) V(r/r^n)=1(r/r^n) - n(rr/r^(n+2))                             

                                b) V (dot) (r/r^n) = (3-n)/r^n                             

                                c) V x (r/r^n) = 0                             

2) show that                             

                                a) V x (V x A) = V(V (dot) A) - V^2A                             

                                b) V (dot) (A x B) = (V x A) (dot) B - A (dot) ( V x B)

Explanation / Answer

2)a)The x component of U X (V X W)  is given by:

uy(vxwy ? vywx) ? uz(vzwx ? vxwz)

                         or

vx(uywy + uzwz) ? wx(uyvy + uzvz)

By adding and subtracting uxvxwx, this becomes

vx(uxwx + uywy + uzwz) ? wx(uxvx + uyvy + uzvz) = (U.W) vx

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