# Find the angle that A makes with the x-axis

1. Mar 11, 2013

### Toranc3

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

A(vector)= (0,9,-2)

Find the angle that A(Vector) makes with the x-axis

2. Relevant equations

3. The attempt at a solution

I have only found the magnitude

A= sqrt[ (0)^2 + (9)^2 + (-2)^2 ] =sqrt(85)

2. Mar 11, 2013

### Staff: Mentor

Do you know some operation to get the angle between two vectors?
Can you express the x-axis as vector?

3. Mar 11, 2013

### Toranc3

I know of the dot product and the cross product.

4. Mar 11, 2013

### Staff: Mentor

Both are possible, the dot product is easier.

5. Mar 11, 2013

### SithsNGiggles

Any vector on the x-axis can be expressed as $\left(?, \;?, \;?\right)$... Can you fill in the blanks?

6. Mar 11, 2013

### Toranc3

No I am not sure. Is it correct to just divide the x-component for vector A by the vectors magnitude and then take the inverse cosine?

arcos( 0/Sqrt(85) ). Would this be the correct way to do this also?

7. Mar 11, 2013

### Karnage1993

Yes, that also yields the correct answer, but it's better if you know how to apply the dot product between two vectors when using the formula with cosine, as SithsNGiggles suggested to find a vector that can represent the x-axis.

8. Mar 11, 2013

### Toranc3

Oh ok. I am not sure how I would use the dot product if there is no vector on the x-axis.

What would I put for the magnitude of x? Would I use the unit vector?

9. Mar 11, 2013

### SithsNGiggles

If you're still having trouble, my next hint would be, What are the y- and z-components of a vector on the x-axis?

10. Mar 11, 2013

### Toranc3

Would they be 0?

11. Mar 11, 2013

### Karnage1993

Yes. And to your other post, the unit vector, ie, [1,0,0], works fine as does any vector that's a multiple of it.

12. Mar 11, 2013

### Toranc3

Oh alright. Are you also saying that [2,0,0] would also work ?

13. Mar 11, 2013

### Curious3141

Yes, but you have to take into account the magnitude of the vector you choose.

(1,0,0) is just easier because the magnitude is 1.

14. Mar 11, 2013

### Toranc3

Alright thank you guys!