The z component of the angular momentum of a particle whose position v

1.	The z component of the angular momentum of a particle whose position vector is
Answer» <P> Solution :Here, `vecr=xhati+yhatj+zhatk` `vecp=p_(x)hati+p_(y)hatj+p_(Z)hatk` `vecp=p_(x)hati+p_(y)hatj+p_(z)hatk` Let `vecL=L_(x)hati+L_(y)hatj+L_(Z)hatk`……………(i) As `vecL=vecr xx vecp = \|{:[hati,hatj,hatk],[x,y,x],[p_(x),p_(y),p_(z)]:}\|` `=hati(yp_(z)-zp_(y))+hatj(zp_(x)-xp_(z))+hatk(xp_(y)-yp_(x))`............(ii) Comparing the COEFFICIENTS of `hati, hatj` and `hatk` in Eqs. (i) and (ii), we GET `L_(x) = yp_(z)-zp_(y)` `L_(y)=zp_(x)-xp_(z)` `L_(z)=xp_(y)-yp_(x)`

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