Question

How do I find the unit vector for `v = < 2,-5,6 >`?

Answer 1

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 `sqrt(65)` to get

`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!