Stupid Question About Finding the Angle of a Vector

In summary, the conversation is about working in the 1st Quadrant of the x-y plane and rotating a vector through an angle while maintaining its magnitude. The question is whether this is a dot product problem and the response is affirmative.
  • #1
Saladsamurai
3,020
7
:smile: Okay then!

Let's say we are ONLY working in the 1st Quadrant of the x-y plane. I have some vector in that region that makes some angle with the +x axis. I then rotate that vector through some angle.

The initial points of the vector before and after are coincident, i.e. I only move the terminal end to some new point while maintaining the vectors magnitude.

I know the initial point, I know the terminal points of both the original and new vector.

I now need the angle that I must have rotated through to get to the new point.

Is this a dot product problem?
 
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  • #2
That's what it is.
 
  • #3
:smile: Alrighty-then!
 

FAQ: Stupid Question About Finding the Angle of a Vector

How do you find the angle of a vector?

To find the angle of a vector, you can use the dot product or cross product formula. The dot product formula is angle = cos^-1 (v * w / |v| * |w|), where v and w are the two vectors and |v| and |w| represent their magnitudes. The cross product formula is angle = sin^-1 (|v x w| / |v| * |w|), where v and w are the two vectors and |v x w| represents the magnitude of their cross product.

Can I use trigonometry to find the angle of a vector?

Yes, you can use trigonometry to find the angle of a vector. You can use the inverse trigonometric functions such as cosine or sine to calculate the angle between two vectors.

What is the difference between the dot product and cross product when finding the angle of a vector?

The dot product is used to find the angle between two vectors in a 2D and 3D space, while the cross product is used to find the angle between two vectors in a 3D space. The dot product yields a scalar value, while the cross product yields a vector value. Additionally, the dot product gives the angle between the two vectors in the range of 0 to 180 degrees, while the cross product gives the angle between the two vectors in the range of 0 to 90 degrees.

Can I use the Pythagorean theorem to find the angle of a vector?

No, the Pythagorean theorem only applies to right triangles and cannot be used to find the angle between two vectors. You will need to use the dot product or cross product formula to find the angle of a vector.

Are there any other methods for finding the angle of a vector?

Yes, there are other methods for finding the angle of a vector, such as using the law of cosines or the law of sines. However, these methods may require additional information such as the length of the vectors and the angle between them. The dot product and cross product formulas are the most commonly used methods for finding the angle of a vector.

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