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

1 Answer
Morgan
Jan 23, 2017

u=<3/7,-6/7,2/7>u=<37,−67,27>

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|)u=v|v|

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

|v|=sqrt((v_x)^2+(v_y)^2+(v_z)^2)|v|=√(vx)2+(vy)2+(vz)2

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

|v|=sqrt(9+36+4)|v|=√9+36+4

|v|=sqrt(49)|v|=√49

|v|=7|v|=7

We now have:

u=(<3,-6,2>)/7u=<3,−6,2>7

=>u=<3/7,-6/7,2/7>⇒u=<37,−67,27>

Hope that helps!

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