# Homework Help: How to find a vector that has the same direction

1. Nov 4, 2007

### baokhuyen

1. The problem statement, all variables and given/known data
Can anyone help me with his problem:
how to find a vector that has the same direction as <-2,4,2> but has length 6

2. Relevant equations

3. The attempt at a solution
the length of that vector is: 6= (-2)^2*a^2+(4)^2*b^2+(2)^2*c^2
Then I don't know what to do next?

2. Nov 4, 2007

### ZioX

Suppose I have a unit vector (a,b,c). What is the length of k(a,b,c)?

3. Nov 4, 2007

### Antineutron

divide the lengh from the original vector, that will give you the unit vector. What do you do with the unit vector to get a lengh of 6 and same direction?

4. Nov 4, 2007

### baokhuyen

k(a,b,c)=(ka,kb,kc)=(-2k,4k,2k)
lenght= root(4k^2+16k^2+4k^2)=6
=> root( 24k^2) =6
=> k*root(24)=6
=>k= 6/root(24)= 3/root6
oh I got it, Thank you very much!! Ziox AND Antineutron

5. Nov 4, 2007

### ZioX

Although you haven't done what we said, that works. Note how this scaling quantity is unique up to +/-. Which makes sense: the direction induced by (-2,4,2) is just a line in R^3.

The scaling value that you actually calculated is the ratio of new length to the original length - dividing by the old and multiplying by the new.