How do you find the magnitude of <-15,-12> and write it as a sum of the unit vectors?
The way to find the magnitude is to take the square root of the sum of the squares of the elements in the vectors.
If a vector is
This is true no matter how many dimensions the vector is (means that the vector can go on forever: <a,b,c,d....> and you are going to do the same)
So for this vector, you can apply that formula:
Unit vector means that you want to have a vector with a magnitude of 1 in the same direction, and you can get that by dividing each element of the vector by the magnitude.
So we have:
Simplifying made it
Hope that helps!