# Math Help - Find a vector v with a given magnitude in the direction

1. ## Find a vector v with a given magnitude in the direction

Find the vector v with magnitude 2.7 in the direction of w = < 1, -2, -1 >

This is what i have so far and i will point out where i am stuck.

$|| w || = \sqrt {1^2 + (-2)^2 + (-1)^2 } = \sqrt 6$

$v = 2.7 \frac{w} {|| w ||}$

so, filling in for w we have

$2.7 ( \frac{1} {\sqrt 6} , \frac{-2} {\sqrt 6} , \frac{-1} {\sqrt 6})$

Now, from here do i just multiply the 2.7 to the numerator?

A Similar problem in my book, the solution manual does something weird and i cant figure it out like

$5 \frac{u} {|| u ||} = 5 < \frac {-1}{\sqrt 5} , \frac{2}{\sqrt5} >$

Then, they go to this final step and i dont see how they are doing that?

$< - \sqrt 5 , 2 \sqrt 5 >$

2. ## Re: Find a vector v with a given magnitude in the direction

Originally Posted by icelated
Now, from here do i just multiply the 2.7 to the numerator?
Yes.

Originally Posted by icelated
A Similar problem in my book, the solution manual does something weird and i cant figure it out like

$5 \frac{u} {|| u ||} = 5 < \frac {-1}{\sqrt 5} , \frac{2}{\sqrt5} >$

Then, they go to this final step and i dont see how they are doing that?

$< - \sqrt 5 , 2 \sqrt 5 >$
Recall that $5/\sqrt{5}=\sqrt{5}$.

thank you

4. ## Re: Find a vector v with a given magnitude in the direction

Originally Posted by icelated
thank you
Use the thanks button, don't just make a post saying thanks

CB