How do you normalize #( - 5 i + 4 j - 5 k )#?

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Answer 1 · 2016-12-29T04:35:24

Normalized vector is #-5/sqrt66hati+4/sqrt66hatj-5/sqrt66hatk#

Normalizing a vector #(-5hati+4hatj-5hatk)# means

a unit vector, whose initial point is same but terminal point is one unit in the same direction.

Hence, for a vector #vecv=ahati+bhatj+chatk#, its normalized vector is #1/|v|(ahati+bhatj+chatk)#, where #|v|=sqrt(a^2+b^2+c^2)#

and for #(-5hati+4hatj-5hatk)#, its normalized vector is

#1/sqrt((-5)^2+4^2+(-5)^2)(-5hati+4hatj-5hatk)#

= #1/sqrt(25+16+25)(-5hati+4hatj-5hatk)#

= #-5/sqrt66hati+4/sqrt66hatj-5/sqrt66hatk#