CHAPTER 02.25: VECTORS: What is the definition of the dot product of two vectors?

 

 

In this segment, weíll talk about what is the definition of dot product of two vectors. So let A be a vector and the components letís suppose are a1, a2, all the way up to a-n. So we have n-vector, n-components n-dimensional vector right here A. And then we have, letís suppose, vector B. We have b1, b2, up to b-n. So you have n-components of that b vector also. So let A and B be two n-dimensional vectors and then the dot product; itís also called inner product, so itís up to you what to call it. So itís called the dot product or the inner product and is defined as follows. Itís defined like this: so all you do is you put a dot in between the two vectors of which youíre trying to find the dot product of and itís nothing but simply multiplying the first component here to the first component. You get a1b1 and then you take the second component here and the second component here and multiply that one and then you keep on doing this to the end. And then you simply add all of them up so youíre multiplying the corresponding components and adding them up. I can write this as a summation, also as sum is equal to i is equal to 1 to n, a sub-i, b sub-i. And thatís how you find the dot product of two vectors.