5. the analytical method of adding vectors expressed in terms of their components may be applied to vectors in three dimensions, for which graphical work is inconvenient. find the magnitude of the resultant of the vectors a = i12 —j37 + k58 and b = i5 + j30 — k42, where i, j, and k are unit vectors along the x, y, and z axes, respectively

The membrane surrounding a living cell consists of an inner and an outer wall that are separated by a small space. assume that the membrane acts like a parallel plate capacitor in which the effective charge density on the inner and outer walls has a magnitude of 7.0 × 10-6 c/m2. (a) what is the magnitude of the electric field within the cell membrane? (b) find the magnitude of the electric force that would be exerted on a potassium ion (k+; charge = +e) placed inside the membrane.

Awave is produced in a rope. the wave has a speed of 33 m/s and a frequency of 22 hz.

Agraduated cylinder contains 63.0 ml of water. a piece of gold, which has a density of 19.3 g/ cm3, is added to the water and the volume goes up to 64.5 ml. calculate the mass in grams of the gold that was added to the water. explain how you got your answer.