Understanding the Right Hand Rule: Vector (AxB)

In summary, the right hand rule can be correctly applied to vectors A and B if they are redrawn with their tails at the same point. This allows for a proper understanding and application of the smallest angle and direction of the vectors. Redrawing the vectors does not alter their direction, but simply repositions them for ease of use in the right hand rule.
  • #1
duplaimp
33
0
Hi,
I have a question about how to apply the right hand rule in this vector (AxB)

5PNOAT8.png


I would say that it is -k (missing ^) because of the smallest angle is the one drawn in red, but it is k. Can anyone explain why?
 
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  • #2
Draw the vectors with their tails at the same point.
 
  • #3
But the vectors are given as I draw
 
  • #4
duplaimp said:
But the vectors are given as I draw
True, but you must redraw them to properly apply the right hand rule. The vectors are both applied at the same point; redraw so that the tails of the vectors emanate from that point.

By redrawing the vectors you are not changing them. You're just sliding the vector A over so that its tail coincides with that of vector B. Sliding vectors around does not change them, as long as they continue to point in the same direction.
 
  • #5


The right hand rule is a convention used in physics to determine the direction of a vector resulting from the cross product of two other vectors. It states that if you point your right thumb in the direction of vector A and your index finger in the direction of vector B, then your middle finger will point in the direction of the resulting vector, AxB. In this case, the smallest angle between vectors A and B is drawn in red, which means that your thumb and index finger will be pointing in opposite directions. This results in your middle finger pointing in the opposite direction as well, giving you a negative (or -k) direction for the resulting vector. It is important to note that the right hand rule is just a convention and the choice of which direction is considered positive or negative is arbitrary.
 

1. What is the right hand rule and how is it used in science?

The right hand rule is a method used to determine the direction of a vector resulting from the cross product of two other vectors. It is commonly used in physics and engineering to calculate the direction of magnetic fields, electrical currents, and torque.

2. How do you use the right hand rule to find the direction of a vector?

To use the right hand rule, start by extending your right hand with your thumb, index finger, and middle finger perpendicular to each other. Then, point your index finger in the direction of the first vector and your middle finger in the direction of the second vector. Your thumb will then point in the direction of the resulting vector.

3. Can the right hand rule be used for vectors in 3-dimensional space?

Yes, the right hand rule can be used for vectors in 3-dimensional space. In this case, the three fingers of your right hand represent the three axes (x, y, and z) and the resulting vector will be perpendicular to both the first and second vectors in the direction determined by your thumb.

4. What is the difference between the right hand rule and the left hand rule?

The right hand rule is used to determine the direction of a vector resulting from a cross product, while the left hand rule is used for vectors resulting from a dot product. Additionally, the direction of the vectors in the two rules are determined by different fingers on the respective hands.

5. Are there any real-life applications of the right hand rule?

Yes, the right hand rule has various real-life applications in fields such as engineering, physics, and computer graphics. It is used to determine the direction of magnetic fields in motors and generators, the direction of torque in rotating objects, and the orientation of 3D objects in computer graphics.

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