Question

What is the norm of `< -3, -1 , -3 >`?

Answer 1

The norm is otherwise described as the normalized version of a vector: a unit vector in the same direction as the original vector. In this case: `<-3/sqrt19,-1/sqrt19,-3/sqrt19>`.

Explanation:

We need to find the length of the initial vector. For a vector `<a, b, c>`

`l = sqrt(a^2+b^2+c^2) = sqrt((-3)^2+(-1)^2+(-3)^2) = sqrt(9+1+9) = sqrt 18`

Then we simply divide each of the 3 elements by this length to yield a unit vector: `<-3/sqrt19,-1/sqrt19,-3/sqrt19>`.