How to find the angle between an XYZ vector and the y-axis? Please help

In summary: It's a multiple choice problem with the choices being:901191516129 I've already tried 2 answers, forfeiting 50% of the potential credit. Is...In summary, if you are trying to find the angle between an XYZ vector and the y-axis, you should use the cross-product of the vectors instead of the dot product.
  • #1
ian_spurlock
14
0
How to find the angle between an XYZ vector and the y-axis? Please help!

Homework Statement



A vector is given as follows:

A = 2i - 2j - 3k

The angle between A and the y-axis is, in degrees, closest to?:

90
119
151
61
29

Homework Equations



c = ab sin[tex]\theta[/tex] ?

The Attempt at a Solution



I tried:

cos[tex]\theta[/tex] = (AdotB)/(A x B)

I tried to set a vector along the y-axis to use as B.

Isolating [tex]\theta[/tex] yielded 56.3 degrees, which is apparently incorrect.
 
Physics news on Phys.org
  • #2


ian_spurlock said:

Homework Statement



A vector is given as follows:

A = 2i - 2j - 3k

The angle between A and the y-axis is, in degrees, closest to?:

90
119
151
61
29

Homework Equations



c = ab sin[tex]\theta[/tex] ?

The Attempt at a Solution



I tried:

cos[tex]\theta[/tex] = (AdotB)/(A x B)

I tried to set a vector along the y-axis to use as B.

Isolating [tex]\theta[/tex] yielded 56.3 degrees, which is apparently incorrect.

Maybe try using the cross-product instead of the dot-product...
 
  • #3


To be honest, I don't know what formula to use and I don't even know if I can use the y-axis as a vector.

I don't want the answer... I just want to know where to start and what procedure I should use.

I'm pretty confused.
 
  • #4


You're just mixing up the dot product and the cross product. You should have

[tex]\vec{A}\cdot\vec{B} = |A||B|\cos \theta[/tex]
[tex]|\vec{A}\times\vec{B}| = |A||B|\sin \theta[/tex]

You can use either to find the angle [itex]\theta[/itex].
 
  • #5


ian_spurlock said:
To be honest, I don't know what formula to use and I don't even know if I can use the y-axis as a vector.

I don't want the answer... I just want to know where to start and what procedure I should use.

I'm pretty confused.

The unit vector in the direction of the y-axis is the j vector. Do you know the equation for the vector cross-product? How could you perhaps use it to find the angle?
 
  • #6


Well like vela posted the cross-product formula is LaTeX Code: [tex]|\vec{A} X \vec{B}| = |A||B|sin \theta [/tex]

But I only have a vector A? Or can I use components of vector A in that formula?
 
Last edited by a moderator:
  • #7


ian_spurlock said:
Well like vela posted the cross-product formula is LaTeX Code: [tex]|\vec{A} X \vec{B}| = |A||B|sin \theta [/tex]

But I only have a vector A? Or can I use components of vector A in that formula?

I tried to clean up your latex -- hope I got it right.

Since you are asked to find the angle with the y axis, you have two vectors. you have A, and you have j. If you cross A into j as vectors, you will get an answer that has the inclusive angle in it. Do you know how to calculate the cross-product using a determinant?
 
  • #8


That part I do know how to do. But if I crossed vectors A and j, wouldn't I just get a vector in some form of i + j + k? How would I calculate an angle from that?
 
  • #9


ian_spurlock said:
That part I do know how to do. But if I crossed vectors A and j, wouldn't I just get a vector in some form of i + j + k? How would I calculate an angle from that?

Use the magnitude equation that you posted a couple steps back. The magnitude of the vector resultant is related to the magnitude of A and j and ...
 
  • #10


Ahh, of sintheta

I'm getting it now.

Is j = (0i -2j + 0k)? Is it as simple as that?
 
  • #11


I tried to solve it as such... and I got 61 degrees which was wrong...
 
  • #12


ian_spurlock said:
I tried to solve it as such... and I got 61 degrees which was wrong...

Post the details of your calculation. Also, make a good sketch for yourself in 3-space, to get an intuitive feel for what the answer should be.
 
  • #13


A = 2i - 2j - 3k ... A = 4.12
j = 0 + 1j + 0 ... j = 1
Code: 
|i   j   k |
|2  -2  -3 |
|0   1   0 |... this matrix yielded [B]N[/B] = 3i + 2k ... N = 3.61
N = Aj sintheta
theta = sin^(-1) (N/Aj) = 61 degrees
 
Last edited by a moderator:
  • #14


ian_spurlock said:
A = 2i - 2j - 3k ... A = 4.12
j = 0 + 1j + 0 ... j = 1
Code: 
|i   j   k |
|2  -2  -3 |
|0   1   0 |... this matrix yielded [B]N[/B] = 3i + 2k ... N = 3.61
N = Aj sintheta
theta = sin^(-1) (N/Aj) = 61 degrees

Yeah, I get the same answer. It's not right? Do they want a couple figures to the right of the decimal point maybe?
 
  • #15


berkeman said:
Yeah, I get the same answer. It's not right? Do they want a couple figures to the right of the decimal point maybe?

Oops, I see it's multiple choice. What does it look like in your sketch?
 
  • #16


It's a multiple choice problem with the choices being:

90
119
151
61
29

I've already tried 2 answers, forfeiting 50% of the potential credit. Is it possible that it is 151 degrees? That is 61+90 degrees... Or 119? 180 - 61?

God I hate Mastering Physics. They gave us a free trial for it as LSU. What's the catch? We're basically beta testers. Infuriating.
 
  • #17


I'm bad at sketching 3d and I really don't know how to interpret my sketch.
 
  • #18


berkeman said:
Oops, I see it's multiple choice. What does it look like in your sketch?

I think the sketch is needed to see the answer. It's over 90 degrees to the positive y axis... Since the answer is multi-valued, our calculators only gave us the value for the first quadrant of the sine function...
 
  • #19


Eh, I am bad at sketching in 3d. What can I say about it really? It's below the XY plane?

Exactly what is theta in this case?
 
  • #20


The answer was 119 apparently. I don't even know why. Maybe my sketch is just extremely difficult to interpret? Blah.

Anyway, thanks for the time and input. At least I have the raw calculation part down.

Thanks a bunch.
 
  • #21


ian_spurlock said:
It's a multiple choice problem with the choices being:

90
119
151
61
29

I've already tried 2 answers, forfeiting 50% of the potential credit. Is it possible that it is 151 degrees? That is 61+90 degrees... Or 119? 180 - 61?

God I hate Mastering Physics. They gave us a free trial for it as LSU. What's the catch? We're basically beta testers. Infuriating.

I think I know which one it is based on my sketch. I've requested help from the other Homework Helpers, to be sure that I'm not leading you astray...
 
  • #22


OK great. I'd like to know how to solve this in case I encounter a problem like this on an exam.
 
  • #23


ian_spurlock said:
OK great. I'd like to know how to solve this in case I encounter a problem like this on an exam.

I'm still hopeful that another HH'er will check all of this. From my sketch, it looks like the 61 degree angle is to the negetive y axis, not the positive y axis. That's why the answer was 180-61, to get the answer to the + y axis. Without the sketch or some other intuition, it would be hard to know that the angle calculated with the cross-product technique is in the first quadrant of the sine function, and may not match the physical situation.
 
  • #24


Well, using the dot product to find theta, isn't it simply because cos(theta) < 0 which only occurs in the second and third quadrants? A sketch, or in this case the multiple choice answers, shows that the angle is in the second quadrant and so the angle is 180 - 61.
 
  • #25


OK that makes crystal clear sense.

I feel kinda dumb for not thinking of that haha. Looooooooong day.

:epic facepalm:

Thanks a lot man. Much obliged.
 
  • #26


And thanks @ Subdot

I'll remember that trick from now on
 

What is an XYZ vector?

An XYZ vector is a mathematical representation of a three-dimensional object, with the X, Y, and Z axes representing the three dimensions.

What is the y-axis?

The y-axis is one of the three axes in a three-dimensional coordinate system, representing the vertical dimension.

How do I find the angle between an XYZ vector and the y-axis?

To find the angle between an XYZ vector and the y-axis, you can use the dot product formula: cos(theta) = (v · w) / (|v| * |w|), where v is the XYZ vector and w is the unit vector along the y-axis. The resulting angle will be in radians.

Can I use a calculator to find the angle?

Yes, you can use a scientific calculator or an online calculator that has a dot product function to find the angle between an XYZ vector and the y-axis.

Why is finding the angle between an XYZ vector and the y-axis important?

Finding the angle between an XYZ vector and the y-axis can be useful in various applications, such as 3D modeling, robotics, and physics, where understanding the orientation of an object or vector is necessary.

Similar threads

Angle between normal force and radial line for cylindrical coordinates
    • Introductory Physics Homework Help
Replies
21
Views
1K
Find the angle between this vector and the coordinate axes
    • Introductory Physics Homework Help
Replies
16
Views
3K
Vector problem -- Find the angle between vector A and vector B
    • Introductory Physics Homework Help
Replies
8
Views
1K
Finding Vector Angle using cosine law
    • Introductory Physics Homework Help
Replies
13
Views
2K
Finding direction of force vector
    • Introductory Physics Homework Help
Replies
3
Views
1K
Finding Vector Components Using Angle and Magnitude | Vector A along Vector B
    • Introductory Physics Homework Help
Replies
2
Views
802
Find Angular Velocity for Moving Particle Parallel to x-Axis
    • Introductory Physics Homework Help
Replies
11
Views
1K
Map question involving vectors (find the angle)
    • Introductory Physics Homework Help
Replies
13
Views
1K
What is the Angle of a Vector with x, y, and z Axes?
    • Introductory Physics Homework Help
Replies
10
Views
1K
Confusion in Adding Vectors: How to Find Missing Magnitudes and Angles?
    • Introductory Physics Homework Help
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top