A $210$ kg rocket in deep space moves with a velocity of $(123\mathrm{.}6$ m$/$s$)$ i$+(38$ m$/$s j$)$ j$.$

Suddenly it explodes into three pieces, with the first $78\mathrm{.}56$ kg moving at $(-321$ m$/$s$)$ i $+(234$ m$/$s$)$ j and the second $55\mathrm{.}26$ kg moving at $(14\mathrm{.}5$ m$/$s$)$ i $+(88\mathrm{.}5$ m$/$s$)$ j$.$

Find the velocity of the third piece.