# Simple Vector Problem

1. Oct 21, 2010

### Loppyfoot

1. The problem statement, all variables and given/known data

Find two vectors, v1, and v2, whose sum is <-4,1,1>, where v1 is parallel to <2,5,-4>, and where v2 is perpendicular to <2,5,-4>

2. Relevant equations

I am guessing I use the cross product for this equation, but I'm confused about how to start this problem.

3. The attempt at a solution

any hlep at all would be greatly appreciated!

2. Oct 21, 2010

### Staff: Mentor

Don't use the cross product.

Write v1 and v2 using coordinates. You're given that they add to <-4, 1, 1>. You're also given that v1 is parallel to <2, 5, -4>, which means that v1 is some constant multiple of <2, 5, -4>. You're also given that v2 is perpendicular to <2, 5, -4>. Two vectors being perpendicular should suggest a particular operation.

3. Oct 21, 2010

### Loppyfoot

So, first I realized that v1= K<2,5,-4>

Then I figured that since v1+v2=sum, ;
then:

<4,1,1> - K<2,5,-4> = v2

Now, what process would I use to find K?

4. Oct 21, 2010

### Staff: Mentor

Then what are the coordinates of v1?

How about finding coordinates for v2 first?

Also what can you do with the given information that v2 is perpendicular to <2, 5, -4>?