A small particle carrying a +50 uC charge moves at 35 m/s through a uniform 0.75

Question

A small particle carrying a +50 uC charge moves at 35 m/s through a uniform 0.75-T magnetic field. The velocity and magnetic field are both in the xy- plane, with the velocity making a 25 degree angle and the magnetic field a 262 degree angle, both measured counterclockwise from the + x axis. Find the magnitude and direction of the magnetic force on the particle.

THIS IS THE FORMAT AT WHICH ALL OF MY PROIBLEMS MUST BE SOLVED AND IT CONFUSES ME.

Structured Problem Solving
A major difficulty that students will often encounter is an inability to approach a problem in a systematic manner. The following procedural method is intended to guide you through solving any physics problem. My further hope is that through using this process you will realize that any problem in life, no matter how difficult is appears to be, can be addressed by breaking it down into steps.
Key Idea: Write down a short statement of the physical principle which you think is the most relevant to solving the problem. Describe the elements of the problem which indicated that this physical principle might be applicable.
Stock of Data: Make a list of the numerical data you are given in the problem description. Be sure to include units. List quantities you are asked to calculate with trailing question marks. This step may include a diagram indicating your understanding of the problem.
I.D. Equation: Choose an equation which reflects both the key idea of your problem and information from your stock of data. You may need more than one equation.
Solve: If the equation or equations you have chosen are not already solved for you unknown then do the algebra to accomplish this now. Be sure to show enough detail in each step so that a reader can follow your work.
Substitute in Numerical Data: Once you have an analytic solution, substitute numerical values into the analytic solution to obtain the final answer.
Sanity Check: Answer the question. “Does this answer make sense in light of the rest of the knowledge I possess?” The sanity check could include a back of the envelope calculation done with a single significant digit or a unit analysis of the final answer.

Explanation / Answer

The magnetic force on a free moving charge is perpendicular to both the velocity of the charge and the magnetic field with direction given by the right hand rule. The force is given by the charge times the vector product of velocity and magnetic field.

F = q [v x B]

Now given, B = 0.75[cos(262) i + sin(262) j] = -0.104 i - 0.7427 j
and v = 35[cos(25) i + sin(25) j] = 31.72 i + 14.791 j
and q = 50*10^-6 C

F = 50*10^-6[[31.72 i + 14.791 j]x[-0.104 i - 0.7427 j]] = 50*10^-6[-23.558k+1.538k] = -1.1 * 10^-3 k N
Mafnitude = 1.1 * 10^-3 N
Direction = along -ve Z axis

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