Find the angle that A makes with the x-axis

[Toranc3]

Homework Statement

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

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

Homework Equations

The Attempt at a Solution

I am not sure how to go about this.

I have only found the magnitude

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

 

[mfb]

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

 

[Toranc3]

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

I know of the dot product and the cross product.

 

[mfb]

Both are possible, the dot product is easier.

 

[SithsNGiggles]

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

 

[Toranc3]

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

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?

 

[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.

 

[Toranc3]

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.

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

AdotX=A*Xcos(theta)


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

 

[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?

 

[Toranc3]

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?

Would they be 0?

 

[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.

 

[Toranc3]

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.

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

 

[Curious3141]

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

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.

 

[Toranc3]

Alright thank you guys!