What is the purpose of a unit vector?

Question

I know this should be very simple to understand but it makes no sense to me.

Why use for example 5i + 6j + 7k ?

And what is a unit vector compared to a normal vector? Online it says they’re used to “specify the direction of a vector” but I just don’t understand what’s meant by that.

In: 5

Answer 1

You can scale groups of vectors up and down and their lengths maintain the same ratio to each other. Rather than specifying a quantity for each vector each time you solve a problem, you can just presume a unit vector length of 1, do the math you want using ratios, then apply these to the quantities in the problem at hand.