# find vector same direction as .. but has length ..

• Sep 9th 2008, 05:51 PM
Craka
find vector same direction as .. but has length ..
Hi having trouble understanding this. Question asks find the vector that has same direction as -2i+4j+2k but that has length 6.

To get the unit vector is did this.
$\displaystyle \begin{array}{l} \hat u = \frac{v}{{||v||}} \\ = \frac{1}{{\sqrt {24} }} < - 2,4,2 > \\ = \frac{1}{{2\sqrt 6 }} < - 2,4,2 > \\ \end{array}$

Then to find the vector in that direction but length 6, I thought you just multiplied the unit vector by 6. So I get this
$\displaystyle \begin{array}{l} = \frac{6}{{2\sqrt 6 }} < 2,4,2 > \\ = 3\sqrt 6 < 2,4,2 > \\ \end{array}$

But the answer is
$\displaystyle \sqrt 6 < - 1,2,1 >$
• Sep 9th 2008, 06:34 PM
skeeter
$\displaystyle \frac{1}{2\sqrt{6}} \langle -2,4,2 \rangle = \frac{1}{\sqrt{6}} \langle -1,2,1 \rangle$

multiply by 6 ...

$\displaystyle \frac{6}{\sqrt{6}} \langle -1,2,1 \rangle = \sqrt{6} \langle -1,2,1 \rangle$
• Sep 9th 2008, 06:43 PM
Craka
Thanks. Was pretty simple algebra. Whoops.