A neutron initially at rest, decays into a proton, an electron and an antineutrino. The ejected electron has a momentum of `1.4xx10^-26` kg-m/s and that of antineutrino `6.4xx10^-27` kg-m/s. Find the recoil speed of the proton a. if the electron and the antineutrino are ejected along the same direction and b. if they are ejected along perpendicular directions. Mass of the proton `1.67xx10^-27`kg.

Explanation

To solve the problem, we will use the principle of conservation of momentum. Let's break it down step by step.

### Given Data:
- Momentum of electron, \( P_e = 1.4 \times 10^{-26} \, \text{kg m/s} \)
- Momentum of antineutrino, \( P_{\nu} = 6.4 \times 10^{-27} \, \text{kg m/s} \)
- Mass of proton, \( m_p = 1.67 \times 10^{-27} \, \text{kg} \)

### Part A: Electron and Antineutrino Ejected in the Same Direction
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