Dot product
Multiplying Vectors: Dot and Scalar Products
There are two types of ways of multiplying vectors: the dot product and the scalar product. The
dot product is written as a dot b, which is a scalar, and the result is a vector. It's easy to see that
multiplication commutes. So a dot a is equal to b dot a. When you multiply a vector by a
constant, one can also see that a dot d is a constant. We can define a coordinate system to
compute the dot products.
Let's choose the coordinate system that is where the x-axis is just along the a vector and then
the y-axis are perpendicular. You're given vectors and you're free to choose any coordinate
system you want. You can use a different coordinate system to compute a dot b. We can find
the components of the components. You are allowed to choose the components, okay, and then
you can choose the coordinates. We need to use some coordinate system. You want to use a
new coordinate system for you to understand what you need to understand. To use it to
understand it, there'll need to find it. We'd like to use the components, and it's easy to find them.
You must choose a new way of multiplying. It is not to multiply the components to multiply. It
doesn't have to multiply a single component. You've got to find a new vector. It needs to multiply
it. A dot d times b is an example. You should use a single element. It means a single vector.
Geometric Definition of Dot Product
A dot b is the length of the vector a times the length of the angle between them. The dot product
is commutative over addition and a scalar can be multiplied against any vector. It's a distributive
over addition, and a scalar can be multiply against any vector. It doesn't matter. It's true in any
coordinate system.
Multiplying Vectors: Dot and Scalar Products
There are two types of ways of multiplying vectors: the dot product and the scalar product. The
dot product is written as a dot b, which is a scalar, and the result is a vector. It's easy to see that
multiplication commutes. So a dot a is equal to b dot a. When you multiply a vector by a
constant, one can also see that a dot d is a constant. We can define a coordinate system to
compute the dot products.
Let's choose the coordinate system that is where the x-axis is just along the a vector and then
the y-axis are perpendicular. You're given vectors and you're free to choose any coordinate
system you want. You can use a different coordinate system to compute a dot b. We can find
the components of the components. You are allowed to choose the components, okay, and then
you can choose the coordinates. We need to use some coordinate system. You want to use a
new coordinate system for you to understand what you need to understand. To use it to
understand it, there'll need to find it. We'd like to use the components, and it's easy to find them.
You must choose a new way of multiplying. It is not to multiply the components to multiply. It
doesn't have to multiply a single component. You've got to find a new vector. It needs to multiply
it. A dot d times b is an example. You should use a single element. It means a single vector.
Geometric Definition of Dot Product
A dot b is the length of the vector a times the length of the angle between them. The dot product
is commutative over addition and a scalar can be multiplied against any vector. It's a distributive
over addition, and a scalar can be multiply against any vector. It doesn't matter. It's true in any
coordinate system.
