Cross Product Confusion

In summary, the conversation discusses a problem with understanding how to compute a cross product for a physics question. The individual is confused about the order of the vectors and the answer provided by the computer. They mention the Biot Savart Law and how it relates to their calculations. The conversation concludes with the suggestion to check the specifications of the computer program.
  • #1
SeannyBoi71
84
0
Hi all,

Just having some trouble understanding a certain example of cross product. It's actually for physics, but figured it belongs in this forum.

In the question I am supposed to cross (dl)y hat with (x1)x hat.

So I go (0 dl 0) x (x1 0 0) = (-x1dl)z hat. But turns out the answer the computer looking for is the same but without the negative. Wouldn't that be the case if i crossed it backwards, i.e. (x1)x hat cross (dl) y hat ??
 
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  • #2
Yes,
[tex](0, dl, 0)\times{(}x_1, 0, 0)=-xdlk[/tex]
and
[tex](x_1, 0, 0)\times{(}0, dl, 0)=xdlk[/tex]
 
  • #3
Well then if that's the case I'm still confused. Because then my answer should be right.
 
  • #4
You need to write the question exactly as it presented, since the cross product depends on which comes first.
 
  • #5
Ok, I am thinking that there is an error in the system, because according to the Biot Savart Law it has a dl x r in the numerator, where r = (x1 0 0) and dl = (0 dl 0). So I computed that but yet my answer was wrong.
 
  • #6
SeannyBoi71 said:
Ok, I am thinking that there is an error in the system, because according to the Biot Savart Law it has a dl x r in the numerator, where r = (x1 0 0) and dl = (0 dl 0). So I computed that but yet my answer was wrong.
Check the computer program specs. Presumably it will tell you how it interprets a cross product for the order in which the vectors are input.
 

1. What is a cross product?

The cross product, also known as the vector product, is an operation in mathematics that takes two vectors and produces a new vector that is perpendicular to both of the original vectors. It is used in geometry, physics, and engineering to calculate torque, momentum, and other physical quantities.

2. How is a cross product different from a dot product?

While the dot product produces a scalar value, the cross product produces a vector. The dot product measures the similarity or projection of one vector onto another, while the cross product measures the perpendicularity or rotation between two vectors.

3. How do I calculate a cross product?

To calculate the cross product of two vectors, you can use the formula:
a × b = (a1b2 - a2b1)i + (a2b3 - a3b2)j + (a3b1 - a1b3)k
where i, j, and k are unit vectors in the x, y, and z directions, respectively.

4. What are some real-world applications of cross products?

Cross products are commonly used in physics and engineering to calculate torque, angular momentum, and electromagnetic fields. They are also used in computer graphics to determine the orientation and direction of objects in 3D space.

5. Can you give an example of cross product confusion?

One common confusion is between the cross product and the cross multiplication method in elementary math. While they both involve the symbol "×", they are completely different operations with different purposes and calculations. It's important to remember that the cross product is a vector operation, while cross multiplication is a method for solving equations with fractions.

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