Exploring Vector Products: Methods and Applications

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In summary, a vector product, also known as a cross product, is a mathematical operation that combines two vectors to create a new vector that is perpendicular to both of the original vectors. It differs from a dot product, which results in a scalar quantity, and has special properties such as being anti-commutative and resulting in a perpendicular vector. To calculate a vector product, the cross product formula is used, and it has various real-life applications such as in physics, magnetic fields, and computer graphics.
  • #1
draotic
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Ways to find vector products??

Homework Statement



can any1 tell me diferent ways to find vector products?

Homework Equations





The Attempt at a Solution


i know this one
AxB=i(a2b3-a3b2)+j(a3b1-a1b3)+k(a1b2-a2b1)
 
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  • #2


There is the way involving the angle between the two vectors (which you have used in some other problems you posted here.)
 
  • #3


Wikipedia says:
[tex]\mathbf{a}\times\mathbf{b}= \begin{vmatrix}
\mathbf{i} & \mathbf{j} & \mathbf{k} \\
a_1 & a_2 & a_3 \\
b_1 & b_2 & b_3 \\
\end{vmatrix}[/tex]
:smile: (but that's equivalent to what you already mentioned)
 

1. What is a vector product?

A vector product, also known as a cross product, is a mathematical operation used to combine two vectors to create a new vector that is perpendicular to both of the original vectors.

2. What is the difference between a dot product and a vector product?

A dot product is a scalar quantity that results from multiplying two vectors, while a vector product creates a new vector. Additionally, the dot product is commutative, meaning the order of multiplication does not matter, while the vector product is anti-commutative, meaning the order does matter.

3. How do you calculate a vector product?

To calculate a vector product, you can use the cross product formula: A x B = AB sinθ n, where A and B are the two vectors, θ is the angle between them, and n is the unit vector perpendicular to both A and B.

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

Vector products are used in many applications, such as calculating torque in physics, determining the direction of magnetic fields, and in computer graphics and 3D modeling.

5. Are there any special properties of vector products?

Yes, one special property of vector products is that the resulting vector is perpendicular to both of the original vectors. Additionally, the magnitude of the vector product is equal to the product of the magnitudes of the original vectors multiplied by the sine of the angle between them.

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