$5.)$ In the diagram below are two separate particles with velocities as shown. There is a magnetic

field of $2\mathrm{.}5T$ pointing in the positive $y-$direction. Particle $1$ has a charge, $q_1=+8\mathrm{.}4C$ and a

velocity $v_1=3\mathrm{.}0{10}^3\frac{m}{s}$ that points in the positive $z-$direction. Particle $2$ has a charge, $q_2=$

$-2\mathrm{.}4C$ and a velocity $v_2=9\mathrm{.}0{10}^3\frac{m}{s}$ that is in the $x-z$ plane at a $30$ with respect to the

positive $x-$axis.

$(40$pts$)$

a$.)$ Write out the velocity for both particles and the magnetic field in unit vector notation.

b$.)$ Calculate the force by putting each velocity and the magnetic field into unit vector notation

and use the cross$-$product. The expression for each velocity and the magnetic field in unit

vector notation must be shown along with all work for the cross$-$products. I will not accept

results from matrix algebra$/$determinants$.$