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
Vectors in general are used to tell direction + magnitude. Lets say you’re standing on a 2D grid at the origin (0,0) where every space is 1 step away. You move over to (5, 6) Your X position moved 5 spaces over and your Y position moved 6 spaces up. You traveled a straight line to that spot though, not 5 steps over then 6 steps up. To get the total distance you traveled you can use the pythagorean theorem to get 7.81 steps. This is the magnitude.
A unit vector is a more specific type of vector. It’s the vector you use when you only care about the direction because it’s magnitude is always 1. Why learn all this crazy math to convert a vector into a unit vector? Well because sometimes we only care about the direction.
Going back to our earlier example. What if someone said “I want to know how to get to a position in the same direction as someone traveling from (0,0) to (5,6), but I want to go 20 steps instead of 7.81.” First you find the unit vector of 5i + 6k, ( 0.64i + 0.77k) and then multiply it by 20 (12.8i + 15.4k).
“I want to go where that ship is heading, but twice as fast”
“I want to compute wind drag on a car as it moves across the map. I know how to compute the magnitude of the drag, I just want to know the unit vector so I can set drag to the opposite direction * magnitude of drag.”
There are plenty of uses for unit vectors.
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