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

When we’re using vectors in normal, 3-dimensional geometry, i, j, and k are typically used to represent unit (ie, length 1) vectors in the positive direction along the x, y, and z axes, respectively.

So 5i + 6j +7k is the vector that points from the origin, (0, 0, 0), to the point (5, 6, 7).