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
If we were to “see” a vector and want to describe which way it’s heading to someone, we might be like “umm, it’s pointing *that direction*”, while pointing in that direction. And *that direction* is vague, isn’t it? People do it all the time – “He drove off that way, and he was going about 50 mph”. This is meaningless if you can’t see where I’m pointing when I say *that way*.
Mathematicians, engineers and physicists are not big fans of vague. So, unit vectors provide us with a concrete way of saying *that way*. The 50 mph is important (magnitude) and the unit vector in that direction tells us the rest
Like someone else said, i, j and k aren’t the only unit vectors, but when combined, they form a pretty convenient way to accomplish all this. And not to drift off topic, but that’s what we mean when we say they form a **basis** for 3-dimensional space – you can describe any direction with these vectors and a little multiplication to scale the result down to a magnitude of 1.
Through this, we can all be on the same page with *that way*.
Latest Answers