Question

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

Answer 1

See below

Explanation:

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!