Happy Friday! I wanted to end my week of fx-991EX Classwiz focus with something that I have been missing – flying. As part of the work I do, I usually travel a bit each month. Whether that is to speak at conferences, work with schools and teachers on math pedagogy, technology, or traveling for vacation, I spend a lot of time on planes. But – as of March, I haven’t traveled once, for obvious COVID19 reasons. And, since schools and teachers are going through so much uncertainty, the professional development I was scheduled to do this summer is cancelled. And who knows when live face-to-face conferences and events will happen again. I am grounded. And I miss it!!
As I looked through the menu options for the fx-991EX Classwiz, I saw the Vector menu, which got me thinking back to high school (yes, a LONG way back!!) where we actually learned about vectors. Adding/subtracting vectors to determine the direction a plane would have to fly to get to it’s destination to account for the impact of the planes velocity and the winds velocity. This clearly stayed with me because it made so much sense and I found it fascinating, and to this day, I think about the calculations that must go on by the pilots and the air-traffic controllers to make sure planes get to their destination, counteract wind, avoid other planes, etc., much of which is connected to vectors. I don’t know why vectors was taken out of the geometry curriculum – I think it is now more in upper level courses, but to me it really should still be included in geometry, which most students still take, because it is so relatable and relevant. Students see planes (even if they don’t necessarily go on them) flying above them, and I think it would be a great way to bring in a very real answer to ‘when are we ever going to use this?” Obviously there are more applications of vectors, but planes is the one that really stuck with me.
But, I digress. Let’s get to the focus of today’s post, which is using the Vector menu on the fx-991EX Classwiz to work with vector problems. I am focusing on simple vector calculations in my video related to determining a planes path based on their velocity and direction and the impact on this from the winds velocity and direction. A vector has both magnitude (length/size) and direction (often includes angle). If visually finding the direction the plane must fly, which is what I remember doing in school, you place the two vectors (wind/plane)(represented by directed arrows for length and direction) head-to-tail, and then construct the resulting vector (basically making a ‘triangle’ (see image 1). We describe each vector by it’s x-vector magnitude, and it’s y-vector magnitude (so (x,y)). We add/subtracting the vectors by adding/subtracting the (x, y) vectors magnitudes of each, which results in the the solution (x,y). To find the magnitude of the resulting vector you would use the (x,y) solution and the Pythagorean Theorem. If you look at the image 2, what you should see a connection to the Pythagorean Theorem and a hint at Trigonometric functions if given angles (if given bearing degrees vs. magnitude of vector). You might have to do some trig to figure out those x- and y- vector magnitudes or the magnitude of a given vector if only given it’s bearing degrees.
There are many applications for vectors (navigation, force, displacement, acceleration, etc). What I show you in this video is how to do vector calculations in 2-dimensions (you can also do vectors in 3 dimensions which would be the same process, just choosing 3 dimensions vs. 2). I show adding/subtracting, scalar multiplication, and also the Dot Product.
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