Find Head of Vector [a,b,c] with Length 3 in Same Direction as [−3,−4,12]

[PiRsq]

The question asked me to find the head of a vector [a,b,c] whose length is 3 and is in the same direction as vector
a=[-3,-4,12]

So I found the follwing:

Let vector x be the unknown vector

|a|=13
|x|=3

Since they are both in the same direction, they both must have the same direction angles right?

So:

Cos alpha = -3/13 which is equal to a/3
Cos beta = -4/13 which is equal to b/3
Cos gamma = 12/13 which is equal to c/3

Then I got the values for a,b and c but the book shows me a different answer. What am I doing wrong here?

 

[Hurkyl]

What values did you get, and what does the book say?

 

[PiRsq]

I found my answer to be correct because I did a similar question and found my method to work. Thx though