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

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

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

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

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