How to Solve Cross and Dot Product Problems with u, v, and w?

In summary, the conversation discusses finding various dot products using given information and rules for manipulating the dot product. The conversation also mentions using LaTeX to properly display mathematical equations.
  • #1
prace
102
0
Ok, this one has really got me...

Suppose that u [tex]\centerdot[/tex] (vXw) = 2.

Find

(a) (uXv) [tex]\centerdot[/tex] w
(b) u[tex]\centerdot[/tex](wXv)
(c) v[tex]\centerdot[/tex](uXw)
(d) (uXv)[tex]\centerdot[/tex]v

Once I understand the what to do with the information given, I am sure the rest of the problems will fall into place, but can anyone help me to get started with this? Thanks

Oh, and just for clarification, the little dots that are out of place there are suppossed to represent the dot product. I used the \centerdot command with LaTeX but for some reason it is not where it should be. I am still pretty new at it. If I figure it out, I will edit the post again. So, for example, (a) is (u cross v) dot w.
 
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  • #3
Try the "\cdot" command. Also "\times".

Daniel.
 
  • #4
Thanks for the link Orthodontist!

Let's give this a try... (u[tex]\cdot[/tex]v)[tex]\times[/tex]w

oop... hmm, still too high...
 
  • #5
You have to write everything in tex in order to make things right.

[tex] \left(\mathbf{u}\cdot\mathbf{v}\right)\times\mathbf{w} [/tex]

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

The cross product is a mathematical operation that results in a vector that is perpendicular to both of the original vectors being multiplied. The dot product, on the other hand, is a scalar quantity that is the product of the magnitudes of the two vectors and the cosine of the angle between them.

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

To calculate the cross product of two vectors, you first need to find the determinant of a 3x3 matrix formed by the coefficients of the two vectors. Then, you can use the right-hand rule to determine the direction of the resulting vector.

3. When should I use the cross product in a problem?

The cross product is often used in physics and engineering to calculate the torque, angular momentum, and magnetic forces of a system. It can also be used to find the area of a parallelogram formed by two vectors.

4. What is the geometric interpretation of the dot product?

The dot product can be interpreted as the projection of one vector onto the other, multiplied by the magnitude of the second vector. This results in a scalar value that represents the amount of "overlap" between the two vectors.

5. Can I use the cross product and dot product in 2D problems?

Yes, both the cross product and dot product can be used in 2D problems. The cross product will result in a vector with a magnitude of 0, as there is no third dimension for the vector to be perpendicular to. The dot product, however, can still be used to calculate the projection and angle between two vectors in a 2D plane.

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