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

• Jan 11th 2012, 02:08 PM
icelated
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.

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

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

so, filling in for w we have

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

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

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

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

$\displaystyle < - \sqrt 5 , 2 \sqrt 5 >$
• Jan 11th 2012, 02:15 PM
emakarov
Re: Find a vector v with a given magnitude in the direction
Quote:

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

Yes.

Quote:

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

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

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

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

Recall that $\displaystyle 5/\sqrt{5}=\sqrt{5}$.
• Jan 11th 2012, 02:21 PM
icelated
Re: Find a vector v with a given magnitude in the direction
thank you
• Jan 12th 2012, 11:51 PM
CaptainBlack
Re: Find a vector v with a given magnitude in the direction
Quote:

Originally Posted by icelated
thank you

Use the thanks button, don't just make a post saying thanks

CB