How do you normalize # (5i- 3j + 12k) #?

1 Answer
Feb 20, 2016

Answer:

Normalizing a vector creates a 'unit vector' 1 unit in length in the same direction as the original vector. In this case the normalized vector is #(5/sqrt178i-3/sqrt178j+12/sqrt178k)# or #(5/13.3i-3/13.3j+12/13.3k)#

Explanation:

Normalizing a vector means dividing each of the elements by the length of the vector.

The length of this vector is #l=sqrt(5^2+(-3)^2+12^2)=sqrt178~~13.3#.

The normalized vector can be represented as #(5/sqrt178i-3/sqrt178j+12/sqrt178k)# or #(5/13.3i-3/13.3j+12/13.3k)#.