Proving a relation between cross and dot products

In summary, the cross product and dot product are two different vector operations with distinct properties and physical significances. The cross product results in a vector perpendicular to the two vectors being multiplied, while the dot product results in a scalar value representing the projection of one vector onto the other. These two operations can also be used to prove relations between vectors and determine if they are orthogonal. Additionally, they can be used in any dimension as long as the vectors have the same number of components. The physical significance of the cross product lies in calculating torque and angular momentum, while the dot product is used in calculating work and energy in physics.
  • #1
Bipolarity
776
2
Another vector identity I have been trying to prove. My textbook lists this identity in "properties of cross products" without proving it. I have been trying to prove it, withou much luck, so some insight is appreciated.

[tex] u \times (v \times w) = (u \cdot w)v - (u \cdot v)w [/tex]

Thanks!

BiP
 
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  • #2
This belongs in the homework section.
 

1. What is the difference between the cross product and the dot product?

The cross product is a vector operation that results in a vector perpendicular to the two vectors being multiplied, while the dot product is a scalar operation that results in a single number representing the projection of one vector onto the other.

2. Can the cross product and dot product be used to prove a relation between two vectors?

Yes, the cross product and dot product can be used to prove a relation between two vectors by using their properties and algebraic equations to show how they are related.

3. How do you determine if two vectors are orthogonal using the cross product and dot product?

Two vectors are orthogonal if their dot product is equal to 0, and their cross product is a vector of magnitude 0.

4. Can the cross product and dot product be used in any dimension?

Yes, the cross product and dot product can be used in any dimension as long as the vectors being multiplied have the same number of components.

5. What is the physical significance of the cross product and dot product?

The cross product has physical significance in calculating torque and angular momentum in physics, while the dot product has physical significance in calculating work and energy in physics.

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