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A particle is moving in a uniform magnetic field. The charge of the particle is -5.60 nC and the magnetic field is vector B = -(1.25 T)k^ . A physicist measures the magnetic force on the particle to be vector F = -(3.40 x 10^{-7}N)î + (7.40 x 10^{-7}N)j^.

1) Given the physicist’s measurement, calculate all the components of the velocity of the particle that you can.

2) Are there components of the velocity that cannot be found by the measurement of the force? Which one(s) and why?

3) Calculate the scalar (dot) product between the velocity and force vectors. What is the angle between those two vectors?

The cross and dot products that are created between two vectors are completely different operations. One of the main variations are:

A dot results in a scalar whereas the cross product produces an vector.

The value of the dot is determined by what is called the cosine angle of the two factors and the value absolute for the cross-product is determined by its sine. The result is greatest in the case of parallel vectors and zero if they’re orthogonal. This is the case for orthogonal vectors, and zero for parallel vectors.

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