# 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