# Find unit vectors that satisfy the given conditions:? The unit vector oppositely directed to (-4i+2j+5k) is ?

The vector given here can be written as

<-4,2,5>

To get a vector in the opposite direction, take the opposite sign of each entry:

<4,-2,-5>

The length of this vector is:

`sqrt(4^2+(-2)^2+(-5)^2)=sqrt(16+4+25)=sqrt(45)=3 sqrt(5)~~6.70820393`

To resize our vector to length 1 (a unit vector), we must divide each entry by 6.7082...

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The vector given here can be written as

<-4,2,5>

To get a vector in the opposite direction, take the opposite sign of each entry:

<4,-2,-5>

The length of this vector is:

`sqrt(4^2+(-2)^2+(-5)^2)=sqrt(16+4+25)=sqrt(45)=3 sqrt(5)~~6.70820393`

To resize our vector to length 1 (a unit vector), we must divide each entry by 6.7082...

Thus:

` <4/(3sqrt(5)),(-2)/(3sqrt(5)),(-5)/(3sqrt(5))>`

We can simplify these, by multiplying each numerator and denominator by `sqrt(5)`

` ` `<(4 sqrt(5))/15,(-2 sqrt(5))/15,(- sqrt(5))/3,>`

Approved by eNotes Editorial Team