1. May 25, 2009

### abhikesbhat

1. The problem statement, all variables and given/known data
Vector B has x,y,z components of 4,6 and 3 respectively. Calculate the magnitude of B and the angles B makes with the coordinate axes.

2. Relevant equations
None

3. The attempt at a solution
I can do the magnitude part which is 7.81, but I don't really understand the angles part. Does it mean what angle it makes with the right triangle 5,6 and sqrt61? Please clarify and thanks!

2. May 25, 2009

### Pengwuino

No, it's asking what angles does that vector make with the x, y, and z-axes. That is, what angle does B make with the vectors (1,0,0), (0,1,0), and (0,0,1).

3. May 25, 2009

### abhikesbhat

Oh wow I'm dumb. Thanks!

4. May 26, 2009

### abhikesbhat

Oh but I still don't get it. I know how you do the angles in 2-d planes, but how do you find it out in the x,y,z plane? I'm sorry, but I'm learning by myself and Chapter 3 does not say anything about angles in the x,y,z plane.

5. May 26, 2009

### Pengwuino

Do you know $$\mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over A} \cdot \mathord{\buildrel{\lower3pt\hbox{\scriptscriptstyle\rightharpoonup}} \over B} = \left| A \right|\left| B \right|\cos \theta$$? This will tell you the angle between any 2 vectors.

6. May 26, 2009

### abhikesbhat

Never knew that. Why would the questions ask me that if they never taught it to me? Is this the dot product?

7. May 26, 2009

### abhikesbhat

Also is there a proof, I can find? Or is it easy enough for me to prove?

8. May 26, 2009

### tiny-tim

Hi abhikesbhat

(4,6,3) is the diagonal of a 4,6,3 rectangular box …

they're asking the angle the diagonal makes with each of the three edges …

so draw the diagonals of the three faces which join at (4,6,3), and make three right-angled triangles: that will give you the angles

9. May 26, 2009

### abhikesbhat

But how? Where it starts from is the bottom, but it has 3 components. Or is it asking the angle where the vector ends?

10. May 26, 2009

### tiny-tim

It's asking for the angle at the origin between the diagonal and one edge …

so that's two sides of a triangle, and you just need to draw in the third side of the triangle, which will be along one of the far faces

11. May 26, 2009

### abhikesbhat

Ok so the right triangle on the xy plane is A=7.81 B=3 so aTan gives us an angle of 21. Is that right?

12. May 26, 2009

### abhikesbhat

Sorry for the impatience, but am I right?

13. May 26, 2009

### diazona

No, I don't think so... why are you using the arctangent?

Personally, I think the vector identity Pengwuino posted is the easiest way to do this problem. You can prove it using the law of cosines, and in turn several proofs of that law are listed on its Wikipedia page.

14. May 27, 2009

### tiny-tim

erm … some of us have to sleep! :zzz:
No, A is the hypotenuse

you need the arc-… ?

15. May 27, 2009

### Wattever

16. May 27, 2009

### abhikesbhat

Ok tiny-tim I had some trouble visualizing it so used real life objects to model. The bottom face or the xz plane has a diagonal of 5 and the vector is 7.81. That makes a right triangle with hypotenuse 7.81 and the bottom side 5. aCos(5/7.81) is 50.19 degrees. Is that right? I'll be patient this time...

17. May 28, 2009

### tiny-tim

Hi abhikesbhat!
Yes, the bottom face has sides of 3 and 4, so the diagonal is 5, and so the cosine is 5/7.81 …

but that's the angle between B and the xz plane

you're asked for the angle between B and each of the three axes

18. May 28, 2009

### abhikesbhat

Hmm I don't get it still. Can show step by step how to get the answer if I get it wrong again? I have been stuck on this for awhile now. For the angle it makes with the x-axis, I got a triangle with hypotenuse 7.81 and bottom side 4. This is aCos(4/7.81), but I don't have a calc right now so the angle is aCos(4/7.81)?

19. May 28, 2009

### tiny-tim

Yes …

the three angles are arccos(4/7.81) arccos(6/7.81) and arccos(3/7.81)

20. May 28, 2009

### abhikesbhat

Oh thanks a bunch tiny-tim! I think I understand now, by picturing a rectangular prism. Thanks!