In summary, a cross-product or vector product is a mathematical operation that combines two vectors to create a new vector perpendicular to both original vectors. It differs from a dot product, which results in a scalar value and measures the similarity between two vectors. A cross-product can only be performed with two vectors, but multiple cross-products can be used to calculate the resulting vector of multiple vectors. Cross-products have practical applications in physics and engineering, such as calculating torque and angular momentum, determining magnetic fields, and analyzing forces in three-dimensional space. However, they are limited to use in three dimensions and the order of multiplication affects the resulting vector.
I just forget the rule here.

I am finding angular momentum by using r x mv

If I am using the determinant to evaluate r cross v, where does the mass come in? Do I just mulyiply the result of r cross v by m?

Or do I distribute m to my vector v and then use those values inside the determinant?

It doesn't matter. m is just a number, so
r x (m v) = (m r) x v = m (r x v)

The cross-product, also known as the vector product, is a mathematical operation used to find the product of two vectors in three-dimensional space. It is commonly used in physics to calculate quantities such as angular momentum, torque, and magnetic fields.

To answer your question, the mass does not come into play when calculating the cross-product of two vectors. The cross-product only involves the vectors themselves and their magnitudes, not their masses. So in your case, you would simply multiply the result of r cross v by the mass to find the angular momentum.

It is important to note that the cross-product is not commutative, meaning the order in which the vectors are multiplied matters. So make sure to pay attention to the order of your vectors when calculating the cross-product.

I hope this clarifies any confusion you may have had about the cross-product. Remember, as a scientist, it is always important to understand the rules and principles behind the calculations we use in our research.

## 1. What is a cross-product in science?

A cross-product, also known as a vector product, is a mathematical operation that combines two vectors to create a new vector that is perpendicular to both of the original vectors. It is commonly used in physics and engineering to calculate forces and torques in three-dimensional space.

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

A dot product is a different mathematical operation that results in a scalar value, while a cross-product results in a vector. The dot product measures the similarity or parallelism between two vectors, whereas the cross-product measures the perpendicularity between two vectors.

## 3. Can a cross-product be performed with more than two vectors?

No, a cross-product can only be performed with two vectors. However, it is possible to perform multiple cross-products in succession to calculate the resulting vector of multiple vectors.

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

Cross-products have several practical applications, such as calculating the torque and angular momentum in rotating objects, determining the direction and strength of magnetic fields, and analyzing the forces on a moving object in three-dimensional space.

## 5. Are there any limitations to using cross-products?

One limitation of cross-products is that they can only be performed in three-dimensional space. They are not applicable in higher or lower dimensions. Additionally, the order in which the vectors are multiplied matters, as the resulting vector will be in the direction of the right-hand rule when the vectors are crossed in order.

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