Angle of vector help

1. Sep 12, 2007

anglum

1. The problem statement, all variables and given/known data
Vector B has x y and z components of 6.7, 4.7, 2.4 and the magnitude of Vector B is equal to 8.599

what is the angle between Vector B and the x-axis. answer in units of degrees

3. The attempt at a solution

i am not sure where to begin on this one... i hate online physics courses BLAH

2. Sep 12, 2007

anglum

can i figure this out wiht a formula or do i need to draw it out?

3. Sep 12, 2007

Kurdt

Staff Emeritus
Have you covered direction cosines of vectors?

4. Sep 12, 2007

anglum

i dont recall covering that

5. Sep 12, 2007

anglum

would i assume 8.599 squared = 6.7squared + A squared
A = 5.39

then use those as the lenghts of the sides for the triangle to use the cosine of the angle to get my answer?

6. Sep 12, 2007

anglum

then solving for that angle i get 38.8162364?

7. Sep 12, 2007

BlackWyvern

Draw a rectangle with the dimensions of the dimensions (lol). Then use pythagoras on the faces to find the angle.

That's THE best way to deal with 3D vectors.

8. Sep 12, 2007

Kurdt

Staff Emeritus
Ok. Consider a vector $\mathbf{a}=(a_1, a_2, a_3)$ and imagine the angles between that vector and the vectors $\mathbf{\hat{i}}$, $\mathbf{\hat{j}}$ and $\mathbf{\hat{k}}$ are $\alpha$, $\beta$ and $\gamma$ respectively. Knowing that the magnitude of the vector is $a$ we can use pythagorean theroem to say that:

$$cos(\alpha) =\frac{a_1}{a}$$

$$cos(\beta) = \frac{a_2}{a}$$

$$cos(\gamma) = \frac{a_3}{a}$$

Thus we note:

$$\mathbf{\hat{a}} = \frac{\mathbf{a}}{|\mathbf{a}|}=cos(\alpha)\mathbf{\hat{i}}+cos(\beta)\mathbf{\hat{j}}+cos(\gamma)\mathbf{\hat{k}}$$

Now knowing thiscan you find the angle between the x-axis and the vector with the information you have?

Last edited: Sep 12, 2007
9. Sep 12, 2007

anglum

i am totally lost on ur idea to draw a rectangle of that... once i draw that rectangle how do i use pythagoras on the faces to find the angle?

10. Sep 12, 2007

anglum

ok KURDT i solved the cos of all 3 of those angles

the first angle is 38.816 degrees
the 2nd angle is 56.867 degrees
the 3rd angle is 73.79337 degrees

correct???

11. Sep 12, 2007

Kurdt

Staff Emeritus
Yeah they look fine. So its relatively simple once you know about direction cosines which very few establishments teach in my experience.

12. Sep 12, 2007

anglum

im not sure my next step once i have those 3 values

13. Sep 12, 2007

BlackWyvern

http://i14.tinypic.com/4y548c8.png

That's what I mean. If you can visualize the vector, you'll be able to solve the problem faster. In an exam, you don't have time to waste.

14. Sep 12, 2007

anglum

kurdt once i solve for those 3 values what step do i take next??

i understand why i get those 3 angles im jsut lost on the last steps i need now

15. Sep 12, 2007

Kurdt

Staff Emeritus
You have the answer. The first angle is the angle between the vector and the x-axis. The second is the angle between the vector and the y-axis and the 3rd is the angle between the vector and the z-axis.

16. Sep 12, 2007

Dick

Do you know dot products? That's a much simpler way out of this mess.

17. Sep 12, 2007

anglum

so from the original problem i posted... .where the angle between Vector B with an arrow drawn over the B and x axis is 38.826 degrees??? becuz when i enter that onto the online classroom it is wrong

18. Sep 12, 2007

BlackWyvern

I get 35.049. Try that.

19. Sep 12, 2007

anglum

i tried that black wyvern and it was incorrect

20. Sep 12, 2007

Kurdt

Staff Emeritus
Thats because the magnitude you gave seems to be slightly out using the components you gave. Check them and make sure they are correct.

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