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The Dot Product of Vectors - Concept

Teacher/Instructor 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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