A charged particle of mass 1 kg and charge 1 C at the point (0, 0, 0) moves with initial velocity vector (0, 1, 1) m/s at t=0 s in a uniform magnetic field with field vector of (0, 0, 1) T at any point in the space.

a) Find the velocity vector of the charged particle by hand.

b) Find the coordinates of the charged particle by hand.

c) Use Matlab to plot the locus of the charged particle from t=0 to 5 s. It is a 3D graph.