Dot product and length of a vector

For multiplying vectors or taking the product, there's actually two ways. 

 

1. The dot product : Vector a dot vector b, each of which has from 1 to n components, are going to be equal to the product of each of their corresponding components.

Note that this is just a number(scalar), not a vector. 

--> So in the dot product, you multiply two vectors and you end up with a scalar value.

 

2. the length of a vector : It just uses double lines around the vector. The length of vector "a" is equal to the square root of each of the terms, each of the components, squared and add it up.

3. The relation between the dot product and the length of a vector : We can write the length in terms of the dot product. It equals the square root of the vector dotted with itself.