Maybe I shouldn't have started this blog now, not with everything that's been going on.

Returning to my discussion of the second meeting of my Electromagnetic Theory class for the first week of classes this third term, there were some problems that dealt with three-dimensional vectors and not just two, but these questions only asked for the x, y and z components and not the magnitude (and especially not the angles) of the resultant.

But I did give them the equation for solving for the magnitude of the resultant vector in three dimensions. This was similar to the Pythagorean equation for two dimensions, with the square of the additional (third) component included.

I also had to give them the three ways of defining the components of a vector in three dimensions (equate the z component to zero and it applied to two dimensions as well).

This is because the convention we used when I taught them mechanics and electricity and magnetism (the letter of the vector variable with a subscript of either x, y or z) is different from the method used in the handouts they have. The method was to use the magnitudes of the components as numeric coefficients of unit vectors x, y and z.

I therefore decided to include the alternative way of writing that as given in the first textbook we used, which is to use unit vectors i, j and k.

At least it was good to see that the students were already familiar with unit vectors, since they knew what to call the carets written above the three, which is a “hat.”

I told them that the next meeting we would be talking about the two means of multiplying vectors.

In the first meeting of my mechanics classes for the second week, I gave them a review of the speed or motion word problems that they used to have in their Mathematical Method 1 classes.

This time though, I had an opportunity to give them a more in-depth discussion on how to solve those types of problems, taking note of the fact that since a vehicle in motion always has average speed, distance traveled and time elapsed, for problems involving two vehicles, one of those quantities is usually equal for both.

I showed them five of the usual scenarios involving two vehicles in constant or average velocity: starting from the same point and traveling in opposite directions, then in the same direction, both ending up a certain distance apart after a certain amount of time, then at different times going in the same direction where one overtakes the other. There was also starting from different points, traveling towards each other and meeting up, then traveling in the same direction and one overtakes the other. Lastly there was traveling the same route at different speeds and, of course, getting different times.

All they had to do was follow the steps I outlined to be able to solve for the required quantity.

And that’s all the time I have for today. I’ll pick up the discussion from this point next time. There’s still the second meeting of Advanced Mathematics for the second week to bring up. For now, class dismissed.