Let u = . Find the unit vector in the direction of u, and write your answer in component form. Can someone please explain how to solve these types of problems?

Question

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Can someone please explain how to solve these types of problems?

phi · Answer

a unit vector has length = 1
to make a vector "unit length" divide each of its components by its original length.
can you do that ?

anonymous · Answer

i.e., find the length (magnitude) of u , then divide each component of u by this magnitude.  your result will be a vector of length 1 in the direction of u

anonymous · Answer

@phi 
so if dividing by one, the answers would be -4 and -3 ?

phi · Answer

the length of vector <x,y> is  $ \sqrt{x^2 + y^2 } $

phi · Answer

the formula is the "distance formula"  you might know, that gives the distance between two points.  A vector as its "tail" at (0,0), and its "head" at (x,y)
and we find the length between those two poinsts

anonymous · Answer

so then it would be 5?

anonymous · Answer

Ohh I see

phi · Answer

yes the length of <-4, -3> is 5  
now divide each number by 5

to check, you can find the length of the new vector.  It will have length = 1