Final answer:
The total force acting on the charge is -14.4 x 10⁻¹⁵ N. The angle between the net force and the positive x-axis can be calculated using the cosine function.
Step-by-step explanation:
a) The total force acting on the charge can be calculated by using the formula F = qE + qv x B, where F is the net force, q is the charge, E is the electric field, v is the velocity, and B is the magnetic field. Plugging in the given values, we get F = (3.2 x 10⁻¹⁹ C)(4i-j-2) + (3.2 x 10⁻¹⁹ C)(2i+3j-k) x (2i+4j+k) T. Simplifying the expression, we find F = (-14.4i - 9.6j) x 10⁻¹⁵N.
b) To find the angle between the net force and the positive x-axis, we can use the dot product of the net force and the positive x-axis. The dot product can be calculated as F dot x-axis = |F| * |x-axis| * cos(theta), where theta is the angle between the two vectors. Since the magnitude of the net force is 14.4 x 10⁻¹⁵ N and the magnitude of the positive x-axis is 1, the equation becomes 14.4 x 10⁻¹⁵ N * 1 * cos(theta). Hence, the angle between the net force and the positive x-axis is theta = cos⁻¹(14.4 x 10⁻¹⁵ N).