How do you find the magnitude of <-15,-12> and write it as a sum of the unit vectors?

1 Answer
May 3, 2017

See below


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 #<a,b>#, then the magnitude #=sqrt(a^2+b^2)#

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:

#sqrt((-15)^2+12^2) = sqrt(225+144) = sqrt369# #=3sqrt41#

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: #<(-45sqrt41)/369, (36sqrt41)/369>#

Simplifying made it #(-5sqrt41)/41, (4sqrt41)/41#

Hope that helps!