How do I find the unit vector for #v = < 2,-5,6 >#?
A unit vector just means a vector whose length equals 1 unit. We want a unit vector u in the v -direction. We will use u = v/|v|.
Note: Any vector parallel to v can be written as c v with real c; if c > 0 this goes in the same direction as v.
The length |v| of a vector v = < x,y,z > is
| v | =
#sqrt(x^2 + y^2 + z^2),#and so
|< 2, -5, 6 >|
#=sqrt(2^2 + (-5)^2 + 6^2)#
#= sqrt(4+25+36)= sqrt(65),#
we can divide v by
#u = <2/sqrt(65),(-5)/sqrt(65),6/sqrt(65)>#
Feel free to approximate this with decimals if asked, but this is the exact "math" answer. dansmath to the rescue!