a) In a circuit under test a resistor, R, is connected in series with a capacitor, C. An a.c. current, i, flows through this RC combination, causing a voltage (VR) of 6V to be developed across the resistor, and a voltage (VC) of 8V to be developed across the capacitor. Assuming that VR is in-phase with i, and V lags VR by 90, draw a vector diagram for this arrangement and then calculate the magnitude of the resultant voltage across the whole RC combination. b) You are measuring the force, F, on an electrical conductor operating in the magnetron of a microwave oven, which is subject to a strong magnetic field. The current may be modelled in three-dimensional space as: 1 = 3i - 5j+7k and the magnetic field as: B = 2i+4j-8k Determine the force, F, as the cross product of the current vector and magnetic field vector, (i.e., find 1 x B). Using a 3-dimensional Cartesian axis system, draw all three vectors, or use software to do so. c) Using the dot product, determine the angle between the current vector and the magnetic field vector.