How do you normalize (-2i- 3j + 2k) ?

1 Answer
Mar 5, 2017

u=<-2/sqrt(17),-3/sqrt(17),2/sqrt(17)>

Explanation:

In normalizing the vector we are finding a unit vector (magnitude/length of one) in the same direction as the given vector. This can be accomplished by dividing the given vector by its magnitude.

u=v/(|v|)

Given v=<-2,-3,2>, we can calculate the magnitude of the vector:

|v|=sqrt((v_x)^2+(v_y)^2+(v_z)^2)

|v|=sqrt((-2)^2+(-3)^2+(2)^2)

|v|=sqrt(4+9+4)

|v|=sqrt(17)

We now have:

u=(<-2,-3,2>)/sqrt(17)

=>u=<-2/sqrt(17),-3/sqrt(17),2/sqrt(17)>

Hope that helps!