Answer:
The z-component of the force is
Explanation:
From the question we are told that
The charge on the particle is
The magnitude of the magnetic field is 
The velocity of the particle toward the x-direction is 
The velocity of the particle toward the y-direction is

The velocity of the particle toward the z-direction is

Generally the force on this particle is mathematically represented as

So we have

substituting values
So the z-component of the force is
Note : The cross-multiplication template of unit vectors is shown on the first uploaded image ( From Wikibooks ).
Answer:
The kinetic energy of the particle will be 12U₀
Explanation:
Given that,
A particle is launched from point B with an initial velocity and reaches point A having gained U₀ joules of kinetic energy.
Constant force = 12F
According to question,
The kinetic energy is
....(I)
Constant force = 12F
A resistive force field is now set up ,
Resistive force is given by,

When the particle moves from point B to point A then,
We need to calculate the kinetic energy
Using formula for kinetic energy

Put the value of 

Now, from equation (I)

Hence, The kinetic energy of the particle will be 12U₀.
Since you are looking for the speed, you need to rearrange the formula which is f = speed / wavelength. That should give you speed = f (wavelength.) All you need to do next is to substitute the value to the following equation. speed = 250 Hz (6.0m) that should leave you with 1500 m/s which is very fast.