CHAPTER 02.25: VECTORS: What is
the definition of the dot product of two vectors? In
this segment, we’ll talk about what is the definition of dot product of two
vectors. So let A be a vector and the components let’s 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, let’s 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; it’s also called inner
product, so it’s up to you what to call it. So it’s called the dot product or
the inner product and is defined as follows. It’s defined like this: so all
you do is you put a dot in between the two vectors of which you’re trying to
find the dot product of and it’s 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
you’re 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 that’s how you find the dot product of
two vectors. |