What is the magnitude of the cross product y cross x?

In summary, the cross product of y and x, in the context of an infinite wire generating a field at point P along the x-axis, is out of the page with a magnitude of yx sin(φ), where φ is the angle between them. In this scenario, φ is equal to 90 degrees.
  • #1
whatisreality
290
1
If I choose the positive y direction to be vertically downwards, and the positive x direction to be to the right, and take the cross product y cross x, then the direction of the resultant is out of the page (if I draw x and y as lines on paper). The magnitude is yx sin(φ), where φ is the angle between them.
I do understand that, but it's been put in a context where I can't find φ. An infinite wire carrying current I in the positive y direction generates a field at P, which is a distance a along the x axis. I want to cross y, which is infinite, with x, which is finite but changing. x is the position vector of point P, relative to the infinite wire. I don't know what to use as the angle between them. Is φ=90°? Is sinφ x/(x2+y2)1/2, by Pythagoras theorem and the geometry of the situation, or should that be a y on the numerator?

My textbook explains this poorly, and I think it's still more maths than physics, but I'm sorry if I posted in the wrong place.
 
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  • #2
Yes your angle would be 90 degrees. In terms of vectors

I = y k

x = x i
 

1. What is the definition of cross product magnitude?

The cross product magnitude, also known as the cross product length, is the numerical value representing the size or length of the vector resulting from a cross product operation between two vectors in three-dimensional space.

2. How is the cross product magnitude calculated?

The cross product magnitude is calculated by taking the product of the length of the two vectors and the sine of the angle between them.

3. What is the significance of the cross product magnitude?

The cross product magnitude is an important quantity in vector operations as it provides information about the direction and strength of the resulting vector. It is also used in many applications such as physics, engineering, and computer graphics.

4. How is the cross product magnitude represented mathematically?

In mathematical notation, the cross product magnitude can be represented as |a x b| or ||c||, where a and b are the two vectors being crossed and c is the resulting vector.

5. Can the cross product magnitude be negative?

Yes, the cross product magnitude can be negative depending on the direction of the resulting vector. The magnitude is always positive if the vectors are crossed in a counter-clockwise direction, but it is negative if crossed in a clockwise direction.

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