Given one cross product, find another cross product

In summary, a cross product is a mathematical operation that results in a vector perpendicular to two original vectors. To find the cross product, you can use a formula that involves the magnitudes and angle between the vectors. It is possible to find multiple cross products for one set of vectors due to the infinite possible unit vectors that are perpendicular. You can use the properties of cross products to find another cross product, which has many real-world applications in fields such as physics, engineering, and computer graphics.
  • #1
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Homework Statement


Calculate the cross product assuming that u X w = <-7,1,8>
Find (-3u + 4w) X w = ?


Homework Equations


I'm not sure. I know you have to relate the cross product to something inorder to find what u and w are, but don't know what equations to use.


The Attempt at a Solution


Don't know where to start
 
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  • #2
I think it is best if you use these 3 characteristics.
1. u x w = u w sin(theta)
2. λu x w = λ (u x w)
3. (u + v) x w= u x w + v x w
 

1. What is a cross product?

A cross product is a mathematical operation that takes two vectors and produces a third vector that is perpendicular to both of the original vectors.

2. How do you find the cross product of two vectors?

To find the cross product of two vectors, you can use the formula: a x b = ||a|| ||b|| sin(θ) n where a and b are the two vectors, ||a|| and ||b|| are their magnitudes, θ is the angle between them, and n is the unit vector perpendicular to both a and b.

3. Can you find multiple cross products for one set of vectors?

Yes, it is possible to find multiple cross products for one set of vectors. This is because there are infinitely many possible unit vectors that are perpendicular to the original vectors, resulting in multiple possible cross products.

4. How do you use one cross product to find another cross product?

To use one cross product to find another, you can use the properties of cross products. One property states that a x (b x c) = (a · c)b - (a · b)c, where a, b, and c are vectors. So if you have one cross product, you can use this property to rearrange the equation and solve for another cross product.

5. Are there any real-world applications of finding another cross product?

Yes, there are many real-world applications of finding another cross product. Some examples include physics, engineering, and computer graphics, where cross products are used to calculate forces, torque, and create 3D graphics respectively.

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