A radioactive nucleus, initially at rest, decays by emitting an electron and a neutrino at right angles to one another. The momentum of the electron is 1.2 X 10-²² kg· m/s and that of the neutrino is 6.4 X 10^-23 kg' m/s. Find the direction and magnitude of the momentum of the recoiling nucleus

Assume, the direction of electron is in the positive x direction while the direction of neutrino is in the positive y direction.
In accordance to the principle of conservation of energy, for the recoiling nucleus, the direction of electron is in the negative x direction while the direction of electron is in the negative y direction.
Therefore the momentum vector p of the recoiling electron would be,
p = - p_xi - p_yj