Hi.  I was wondering if someone would please help me with this problem.  Let the vectors u=(-3,4) and v=(5,-2).  Find |2u-v|.  Thank you!  :)

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to evaluate the magnitude of the new vector `2bar u - bar v` , hence, you need to evaluate it, such that:

`2bar u - bar v = 2*<-3,4> - <5,-2>`

`2bar u - bar v = <-6,8> - <5,-2> => 2bar u - bar v = <-6-5, 8-(-2)>`

`2bar u - bar v = <-11,10>`

Evaluating the magnitude of vector `2bar u - bar v` yields:

`|2bar u - bar v| = sqrt((-11)^2 + 10^2)`

`|2bar u - bar v| = sqrt(221)`

Hence, evaluating the magnitude of vector 2bar u - bar v yields `|2bar u - bar v| = sqrt(221).`

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pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

We have  given vectors u=(-3,4) and  vector v=(5,-2).  Find |2u-v|.

Sol. we have

2u=(-6,8)

-v=(-5,2)

Thus

2u-v=(-6,8)+(-5,2)

=  (-11,10)

`|2u-v|=sqrt((-11)^2+10^2)`

`=sqrt(121+100)`

`=sqrt(221)`

`=14.87`  approx

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