35.)+Addition+and+Subtraction+of+two+Vectors+to+Find+the+Resultant+Vector.

=//**__Given two geometric vectors, draw resultant sum and difference vectors.__**//= //**__--__**//

===__Why I chose this section:__ The vector section was actually one of the more interesting units of the course, so I was happy to choose it. I enjoy how it employs a lot of fundamental geometry skills, like being able to use tools to successfully draw and combine or subtract angle measures. There aren't any formulas or calculations, just angle and length measures, so it's an enjoyable and refreshing change. The unit didn't seem challenging right away, because it had a lot of review aspects to it; however, in the end, there were a couple things which proved to have some difficulties. When learning the unit, subtracting the vectors was tricky, and so was changing the vector via multiplication or division. With some practice however, it was easy to get the hang of, and now it comes second nature.=== __--__ =NOTE: Before you begin, your'e going to need a couple materials in order to successfully draw and add and subtract vectors. Be sure to have these tools with you when doing your drawings:= A **RULER:---**And a **PROTRACTOR:** NOTE: use this kind of ruler:

When you have both tools with you, then you are ready to begin!
__--__ =__Adding and Subtracting Vectors__=

First, we must begin with two vectors, like the ones shown below:


The first __step__, is to take each vector, and find its angle in standard position. for this, simply draw a horizontal line at the base, or tail of the vector, and use the protractor to measure the angle:



__Step__ number two is to find the magnitude of each vector. Mathematically speaking, a magnitude of a vector is simply its length, speed, force, etc. of the vector. since the context here doesn't involve any speeds or forces, we simply take the vector ray, and measure the length of it from the arrow tip (head) to the base (tail): Here is a picture of one of the vectors being measured for both angle and and magnitude:

For this vector, I got an angle of 142 degrees, and a magnitude of 7.2 cm. for the other one, I got an angle of 65 degrees and a magnitude of 5.5cm.

After that, the third step is to combine the vectors, from head to tail, and draw the resultant vector, from the base of the bottom vector to the head of the top one. then take measurements of this vector's angle and magnitude.

And this is your resultant vector. it has an angle of 151 degrees and a magnitude of 2.6cm

For subtracting vectors, do the same thing, except for one thing. with the top vector (the one with the other vectors head connected to its base), rotate it around 180 degrees, and then draw the resultant vector. that would look like this: from here you would just solve it normally.

One Last Thing: There are also transformations that can be done to the magnitude: for example, if there were vectors A and B, then A + 2B means that you double the magnitude for vector B. Simple.

Now use these vectors to try some practice problems!



1.) A + C 2.) 2B -A 3.) 1/2B+2C 4.) C-1/3A

For More Help, See This Video VIDEO: http://screencast-o-matic.com/watch/clf1cGkuy

Sources: [] [] [] Most of the vector photos I used Smart notebook for, and uploaded them with edited screen shots.