How do you normalize # (-300i + 200j - 150k)#?

1 Answer
David G.
Apr 28, 2016

The normalised vector is: #((-300/390.5)i+(200/390.5)j-(150/390.5)k)#, which can also be expressed as #(-0.77i+0.51j-0.38k)#

Explanation:

Normalising a vector involves dividing each of its elements by the length of the vector. This yields a vector in the same direction as the original vector, but one unit in length.

First we find the length of the vector:

#l=sqrt((-300)^2+200^2+(-150)^2)=sqrt(90000+40000+22500)#
#=sqrt(152500)~~390.5# #units#

The normalised vector, then, is:

#((-300/390.5)i+(200/390.5)j-(150/390.5)k)#

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