An electron follows a helical path in uniform magnetic field given by `vec(B) = (20 hat(i) - 50 hat(j) - 30 hat(k))` mT. At time t = 0, the electrons velocity is given by `vec(v) = (40 hat(i) - 30 hat(j) + 50 hat(k))` m/s. (a) What is the angle `phi` between `vec(v)` and `vec(B)` ? The electron's velocity changes with time. Do (b) its speed and (c ) the angle `phi` change with time? (d) What is the radius of the helical path ?

Explanation

To solve the problem step by step, we will address each part of the question systematically.

### Given Data:
- Magnetic Field: \(\vec{B} = (20 \hat{i} - 50 \hat{j} - 30 \hat{k})\) mT
- Velocity of Electron: \(\vec{v} = (40 \hat{i} - 30 \hat{j} + 50 \hat{k})\) m/s

### Part (a): Finding the angle \(\phi\) between \(\vec{v}\) and \(\vec{B}\)

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