How do you normalize #<3, -6, 2>#?

1 Answer
Jan 23, 2017

Answer:

#u=<3/7,-6/7,2/7>#

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=<3,-6,2>#, we can calculate the magnitude of the vector:

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

#|v|=sqrt((3)^2+(-6)^2+(2)^2)#

#|v|=sqrt(9+36+4)#

#|v|=sqrt(49)#

#|v|=7#

We now have:

#u=(<3,-6,2>)/7#

#=>u=<3/7,-6/7,2/7>#

Hope that helps!