Question

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

Answer 1

`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!