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# The Dot Product of Vectors - Concept

###### Norm Prokup

###### Norm Prokup

**Cornell University**

PhD. in Mathematics

Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.

An operation used frequently on vectors is the vector dot product, sometimes known as the scalar product. The vector dot product is an operation on vectors that takes two vectors and produces a scalar, or a number. The **vector dot product** can be used to find the angle between two vectors, and to determine perpendicularity. It is also used in other applications of vectors such as with the equations of planes.

A really important topic is the dot product, the dot product is a way of multiplying 2 vectors let's suppose we have vectors u=u1u2 and v=v1v2 in component form their dot product is defined as u.v=u1v1+u2v2 this is the product of the first components plus the product of the second components. Let's try it in an example, I have u=3 negative 4 and v=5 2, u.v equals 3 times 5 plus negative 4 times 2. Actually you might notice that using a dot for a multiplication of scalars is no longer a good idea because it can be confusing so I'm going to actually use parentheses here instead of the dot. Okay this gives me 15 plus negative 8, 15-8 7. So notice when you calculate the dot product of 2 vectors you get a number a real number, a scalar so sometimes this is called the scalar product but just remember that's one of the strange things about the dot product is you're multiplying 2 vectors and getting a real number result.

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###### Norm Prokup

PhD. in Mathematics, University of Rhode Island

B.S. in Mechanical Engineering, Cornell University

He uses really creative examples for explaining tough concepts and illustrates them perfectly on the whiteboard. It's impossible to get lost during his lessons.

Thiswas EXCELLENT! I am a math teacher and have been looking for an easy/logical way to explain the lateral area of a cone to my students and this was incredibly helpful, thank you very much!”

I just learned more In 3 minutes of polygons here than I do in 3 weeks in my math class”

Hahaha, his examples are the same problems of my math HW!”

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