$(2$ pt$)$ A $900$ lb space vehicle traveling with a velocity $v_0=(1500f\frac{t}{s})hat(k)$ passes through the origin $O.$ Explosive charges then separate the vehicle into three parts $A,B,$ and C$,$ with masses $150lb,300lb,$ and $450$ lb respectively. Knowing that shortly therafter the position of the three parts are $A(250,250,2250),B(600,1300,3200)$ and $950,1900$ respectively, where the coordinates are expressed in feet, that the velocity of $B$ is $v_B=(500f\frac{t}{s})hat(i)+(1100f\frac{t}{s})hat(j)+(2100f\frac{t}{s})hat(k)$ and that the $x-$component of the velocity of $C$ is $-400f\frac{t}{s},$ determine the velocity of part $A.$