A uniform shell explodes into three equal parts .Two of the parts fly off perpendicularly to each other with velocities 9m/s and 12m/s. Find the velocity of the third part.😕📖Please solve this.☺

If assumed that the shell was in rest before explosion, then momentum=mv=0. According to the law of conservation of momentum, the final momentum of all three parts collectively must be 0.
Using vector rules,the resultant between the 2 pieces A(with v=9m/s), and B(with 12m/s) is C(with 15 m/s),with direction about 20 degrees from B.
To nullify C then the other part of shell, say D, should be kept 180 degrees to the opposite direction and must have velocity 15 m/s.