# Homework Help 3D vectors problem solving

1. Feb 24, 2013

### 16leafs

Homework Help!! 3D vectors problem solving!!

1. The problem statement, all variables and given/known data
the vector v=(1,√2,c) makes an angle of 60° with the positive z-axis. Determine the angles that v makes with the positive x-axis and the positive y-axis. Explain how many answers there are.

2. Relevant equations
dot product, geometry, cosine,sine,tan

3. The attempt at a solution
I started by drawing the 3D vector with the x,y,z axis's and place a point on the z axis for c. I then tried using geometry with the 60 degrees and the drawn vector to find other angles and also used cosine, sine and tan with the values 1 and root 2. None of the methods seemed to work and am very confused as to what I should do next.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 24, 2013

### tiny-tim

welcome to pf!

hi 16leafs! welcome to pf!
the angle between (1,√2,c) and (0,0,1) is 60°

so use the formula for the angle between two vectors!

3. Feb 24, 2013

### Staff: Mentor

Re: Homework Help!! 3D vectors problem solving!!

start with the dot product of z dot v = |z| |v| cos (60) and recall that z is a unit vector and that cos(60) = 1/2 then solve for c

Now can you see how many solutions for c there from the |z| |v| cos(60) equation?

4. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

thanks for the replies, I really appreciate the help. I'm still confused as to why you gave c a value of unit vector one though?

5. Feb 24, 2013

### Dick

Re: Homework Help!! 3D vectors problem solving!!

You can choose z to be any vector along the positive z axis. It doesn't really matter, but picking z=(0,0,1) would be the simplest choice, yes?

6. Feb 24, 2013

### Karnage1993

Re: Homework Help!! 3D vectors problem solving!!

The value for c would actually be different if you chose the vector [0,0,2] as for the positive z-axis. However, I believe the angles would all be the same.

7. Feb 24, 2013

### Dick

Re: Homework Help!! 3D vectors problem solving!!

Nah, if you put z=[0,0,2] in then you get 2c in the dot product. But |z|=2. They'll just cancel out.

8. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

ok (0,0,1) would seem the simplest, but how would i use the dot product method to solve for c because when i tried using (0,0,1), and then (0,0,2) i got different answers?

9. Feb 24, 2013

### Karnage1993

Re: Homework Help!! 3D vectors problem solving!!

Yup, you're right. I was doing sqrt(2) for the magnitude for some reason.

@16leafs, you solve for c by doing

$[1, \sqrt{2},c] \cdot [0,0,1] = ||[1, \sqrt{2}, c] || \cdot ||[0,0,1]|| \cos{60}$

10. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

When i simplify the equation, the c is cancelled out and im left with no variable?

11. Feb 24, 2013

### Dick

Re: Homework Help!! 3D vectors problem solving!!

12. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

[1,2√,c]⋅[0,0,1]= (1)(0)+(2√)(0)+(c)(1)= c

lzl=√1^2= 1

lvl= √(1^2+√2^2+c^2)= (√3)c

c=(√3)c*1*cos60

Im using equations we have used in class but it doesnt seem to work with c variable on both sides

13. Feb 24, 2013

### Dick

Re: Homework Help!! 3D vectors problem solving!!

sqrt(1+2+c^2)=sqrt(3+c^2). That isn't equal to sqrt(3)*c.

14. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

so its √3+c? giving me c=(√3+c)*1*cos60 which c's will still cancel?

15. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

sorry they dont cancel. so c=√3?

16. Feb 24, 2013

### Dick

Re: Homework Help!! 3D vectors problem solving!!

No offense, but your algebra is atrocious. You get c=sqrt(3+c^2)*1*cos(60). Figure out what cos(60) is and try to solve for c.

17. Feb 24, 2013

### Karnage1993

Re: Homework Help!! 3D vectors problem solving!!

No, √(3 + c^2) ≠ √3 + c. Just leave it as √(3 + c^2) since you cannot simplify it any more. From here, trying squaring both sides.

18. Feb 24, 2013

### 16leafs

Re: Homework Help!! 3D vectors problem solving!!

c^2=3/2+0.5c^2

0.5c^2=3/2

c=√3?

19. Feb 24, 2013

### Karnage1993

Re: Homework Help!! 3D vectors problem solving!!

No, that's not right. When I said square both sides, I didn't say to ignore the 1/2 that was from the cos(60). You still need to square that. Come on!