Tuesday, January 24, 2017

Advanced Math Solutions – Vector Calculator, Advanced Vectors

In the last blog, we covered some of the simpler vector topics. This week, we will go into some of the heavier vector topics. This includes dot product, cross product, and projection. So let’s hop into it.

























Let’s see some examples using the dot product . . .
First example (click here):



Next example (click here):




Now, we will learn about cross product. In multiplication, we often see 1×1 or 1∙1, which both equal the same thing. However, these symbols are very different when talking about vectors. It is important to not interchange the symbols.
















While finding the cross product of two vectors, it is important to know what direction the cross product of the two vectors will point. This is where the right hand rule comes into play.








We’ll go over some properties of cross products.














Now that you have a brief overview on cross products, here’s an example on how to find the cross product of two vectors (click here):




When finding the cross product of two vectors, I find it easier to make a matrix and derive the answer from the matrix, rather than memorizing the formula for the answer.


Onto the last topic, projection . . .












Simple enough, let’s see an example (click here):




In this blog post, we learned about three heavy vector topics. The key to being successful in these topics is to memorize the formulas. If you do that, this will be a piece of cake. Use the definitions, properties, and facts to familiarize yourself with how to find if two vectors are orthogonal or parallel; these tend to be teachers’ favorite questions.

Until next time,

Leah

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