Is the Vector Product Really a Vector?

  • Thread starter Thread starter golshah
  • Start date Start date
  • Tags Tags
    Physics
AI Thread Summary
The discussion centers on proving that the vector (cross) product is indeed a vector in the context of physics and mathematics. It highlights that the cross product's definition leads to a resultant vector that is orthogonal to the two input vectors, which aligns with the characteristics of a vector. Participants question the criteria for defining a vector, such as transformation rules and properties that must be satisfied. The conversation emphasizes the importance of understanding these definitions and properties to validate the nature of the cross product. Ultimately, the discussion seeks clarity on the foundational aspects that classify the cross product as a vector.
golshah
Messages
1
Reaction score
0

Homework Statement

How can I prove that the vector (cross or external) product is really and physically a vector. I face with this problem in math physics course.
thanks for your hint.


Homework Equations





The Attempt at a Solution

 
Physics news on Phys.org
I think the fact that the crossproduct is a vector follows immediately from the definition of the cross product.
 
you find torque with the cross product you need two vectors in order to find it and the resulting torque is normal to the other 2
 
What are you using as a definition of a vector? For example, does a vector obey a certain transformation rule? Does the cross product satisfy the required properties.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggling to understand the concept of this question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Writing a vector parallel and normal to a unit vector ##\hat n##
Replies
26
Views
1K
Difference between scalar and cross product
Replies
5
Views
1K
Finding the Scalar Triple Product of Three Vectors
Replies
2
Views
1K
Syntax Error? x and y components of E field in unit vector form
Replies
13
Views
2K
Vector problem -- Find the angle between vector A and vector B
Replies
8
Views
2K
Generalized coordinates- scalar product
Replies
1
Views
1K
The derivative of the dot product "distributes" over each vector
Replies
5
Views
700
Coupled oscillator question
Replies
2
Views
670
Kepler's Second Law with Angular Momentum
Replies
2
Views
1K
Suvat vector versus the scalar form
Replies
44
Views
4K

Hot Threads

Recent Insights

Back
Top