# Math Help - purpose of unit vector

1. ## purpose of unit vector

hey everyone,

so i've been doing vectors for quite some time now and eventhough i excel at vectors and calculus 3, what exactly is the point of having unit vectors. Why can't we just right them as normal vectors especially when i get to binormals and stuff, they always want unit vectors. Also, if you take the cross product of two unit vectors, do you end up with a unit vector. if not, can you please explain why not

Thanks alot

2. ## Re: purpose of unit vector

Originally Posted by ubhutto
what exactly is the point of having unit vectors. Why can't we just right them as normal vectors especially when i get to binormals and stuff, they always want unit vectors. Also, if you take the cross product of two unit vectors, do you end up with a unit vector. if not, can you please explain why not
Unit vectors are used to standardize measurements.

Let $u = \frac{1}{{\sqrt {14} }}\left\langle {1,2,3} \right\rangle~\&~ v = \frac{1}{{\sqrt 5 }}\left\langle { - 2,0, - 1} \right\rangle$

What does $u\times v=?$.

3. ## Re: purpose of unit vector

unit vectors serve as a basis wrt which other vectors can be expressed. They are usually used as a unit orthogonal (orthonormal) basis ( a.a=1, a.b=0) , in which case the length of any vector is the sum of the squares of it's components.