I Wanna Know

1. Oct 6, 2004

physicsss

how to do this problem:
Let vector V = 36 i + 24 j - 57 k. What angles does this vector make with the x, y, and z axes?

TY

2. Oct 6, 2004

Gokul43201

Staff Emeritus
What do you think ? Any ideas ?

3. Oct 6, 2004

arildno

Do you know what the dot product (scalar product) is?

4. Oct 6, 2004

physicsss

Yea, I know what they are...but aren't they for when you have 2 vectors?

5. Oct 6, 2004

arildno

What makes you think you haven't two vectors at your disposal?

6. Oct 6, 2004

physicsss

Can you expand on it more? The problem only gave me one.

7. Oct 6, 2004

arildno

Well, does there exist, for example, a vector which is parallell to the x-axis, so that you could use this in calculating angle between the given vector and the x-axis?

8. Oct 7, 2004

physicsss

Could you show me an example? (maybe find the angle a 3-d vector (doesnt have to be mine) makes with the x-axis?)

9. Oct 7, 2004

arildno

What does this symbol stand for?

10. Oct 7, 2004

physicsss

i is the x-component, j is the y-com, and k is the z-com.

11. Oct 7, 2004

ComputerGeek

12. Oct 7, 2004

arildno

$$\vec{V}=36\vec{i}+24\vec{j}-57\vec{k}$$
$$\vec{i}$$ is a unit vector PARALLELL to the x-axis, the number multiplied with it is the vector's component along the x-axis (that is, the vector's x-component).
Another way of saying this, is that:
$$\vec{V}\cdot\vec{i}=36$$
Are you now able to calculate the angle?

13. Oct 7, 2004

physicsss

I just began learning dot products, and I have never done such an operation like this...

14. Oct 7, 2004

TenaliRaman

physicssss,
i denotes a unit "vector" along x-axis
j denotes a unit "vector" along y-axis
k denotes a unit "vector" along z-axis

if u find angle of x with i , then with j and then with k ....
what will u have eventually?

-- AI

15. Oct 7, 2004

physicsss

what is x in this case? I'm really confused...

16. Oct 7, 2004

arildno

physicsssssss, TenaliRaman blundered, his sentence should read:
"if u find angle of V with i , then with j and then with k ....
what will u have eventually?"
Does this clear up?

17. Oct 7, 2004

physicsss

not really...is there a formula for finding the angles a vector makes with the axes??

18. Oct 7, 2004

arildno

But the i-vector lies along the x-axis!!
So the angle between the vector V and the x-axis must be the same as the angle between i-vector and V