Before explosion linear momentum was zero, as there is no external impulse on the system so linear momentum should be zero just after explosion.
` vecP_(1) + vecP_(2) +vecP_(3) = 0`
` implies 1 xx 12 hati + 2 xx 8 hatj + vecP_(3) = 0`
` vecP_(3) = - (12 hati + 16 hatj)`
`P_(3) = sqrt(12^(2) + 16^(2)) = 20 kg ms^(-1)`
`m_(3) = (P_(3))/(v_(3)) = 5 kg`