How do you normalize #(- 7 i -j -25k)#?

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Answer 1 · 2017-05-02T01:57:41

# 1 / (15sqrt(3)) (-7hati-hatj-25hatk)#

A normalised vector is just the vector divided by its metric norm, so that the norm of the new scaled vector is unity:

Let:

# vec u = -7hati-hatj-25hatk#

So the metric norm is given by:

# || bar u || ^2 = (-7)^2+(-1)^2+(-25)^2 #
# " " = 49+1+625 #
# " " = 675 #

# :. || bar u || = 15sqrt(3) #

And so:

# hatbaru = (baru) / (|| bar u ||) #
# \ \ = (baru) / (15sqrt(3)) #
# \ \ = 1 / (15sqrt(3)) (-7hati-hatj-25hatk)#