Find a vector that has the same direction as < -2, 4, 2> but has length 6. This probably has something to do with the magnitude and I get sqroot(24) but where do they get the 6?

Thank you.

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- Feb 23rd 2008, 12:26 PMUndefdisfigureSimple question that I am too lazy to analyze...
Find a vector that has the same direction as < -2, 4, 2> but has length 6. This probably has something to do with the magnitude and I get sqroot(24) but where do they get the 6?

Thank you. - Feb 23rd 2008, 12:54 PMPlato
What an honest title!

Here is a short answer: multiply by $\displaystyle \frac{{\sqrt 6 }}{2}$. - Feb 23rd 2008, 07:17 PMJen
So Plato essentially gave you the answer, but just in case you decide that you aren't too lazy to want to know how...

In order to get a vector with different magnitude but in the same direction, find the unit vector in that direction (i.e. multiply the original vector by 1/the magnitude), then multiply the new unit vector by the magnitude that you want it to be.

so in this case you had <-2,4,2>, to get the unit vector we take the magnitude, $\displaystyle \sqrt{(-2)^2+4^2+2^2}=\sqrt{24}=2\sqrt{6}$

Then mutliply your original vector by 1 over this, which is $\displaystyle \frac{1}{2\sqrt{6}}=\frac{\sqrt{6}}{12}$.

we are going to then multiply our vector by this to get the unit vector but since we are going to then multiply the unit vector by 6 to get the new magnitude we can just say $\displaystyle 6(\frac{\sqrt{6}}{12})<-2,4,2>=\frac{\sqrt{6}}{2}<-2,4,2>=<-\sqrt{6},2\sqrt{6},\sqrt{6}>$

(Rock)

Hope that helps!!! - Feb 24th 2008, 02:53 AMmr fantastic