Friday, January 25, 2013

`||bbv|| = 3, bbu = ` Find the vector `bbv` with the given magnitude and the same direction as `bbu`.

You need to find the component form of the vector `v = <a,b>` , hence, you need to use the information provided.


You need to evaluate the magnitude |v|, such that:


`|v| = sqrt(a^2+b^2)`


`3 = sqrt(a^2+b^2)`


The direction angle of the vector coincides to the direction angle of the vector `u = <-12,-5>` ,such that:


`tan theta = b/a => tan theta = 5/12 => b/a = 5/12 => b = a*5/12`


Replacing `a*5/12` for b yields:


`3 = sqrt(a^2+a^2*25/144)=> 3 = +-13a/12=> a = +-36/13 `


`b = +-(36/13)*(5/12)`


`b = +-15/13`


Hence, evaluating the components of the vector v, yields `<+36/13 ,15/13>` or `<-36/13 ,-15/13>.`

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