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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