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

1. ## 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.
$
\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
$
\begin{array}{l}
= \frac{6}{{2\sqrt 6 }} < 2,4,2 > \\
= 3\sqrt 6 < 2,4,2 > \\
\end{array}
$

$
\sqrt 6 < - 1,2,1 >
$

2. $\frac{1}{2\sqrt{6}} \langle -2,4,2 \rangle = \frac{1}{\sqrt{6}} \langle -1,2,1 \rangle$

multiply by 6 ...

$\frac{6}{\sqrt{6}} \langle -1,2,1 \rangle = \sqrt{6} \langle -1,2,1 \rangle$

3. Thanks. Was pretty simple algebra. Whoops.

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# find vector that has the same direction as(2,4,-2) but has length 6

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