Where did the blue box vector come from in the vector multiplication problem?

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SUMMARY

The discussion centers on the origin of the blue box vector in the vector multiplication problem related to the equation RAO = b(Sinβj + Cosβk). The user expresses confusion regarding the derivation of this vector, specifically questioning the transition from the red box vector ω to the blue box vector. A participant clarifies that the blue box vector is derived from the calculation of the vector cross product ω × rAO, divided by the scalar factor b, which was omitted in the intermediate steps. This highlights the importance of maintaining clarity in vector operations and scalar factors during calculations.

PREREQUISITES
  • Understanding of vector operations, specifically cross products.
  • Familiarity with vector notation and components (e.g., j and k unit vectors).
  • Knowledge of the vector triple product identity: A x (B x C) = (A•C)B - (A.B)C.
  • Basic grasp of scalar multiplication in vector equations.
NEXT STEPS
  • Review vector cross product calculations in 3D space.
  • Study the implications of scalar factors in vector equations.
  • Learn about the vector triple product and its applications in physics.
  • Explore examples of RAO calculations in engineering contexts.
USEFUL FOR

Students and professionals in physics and engineering, particularly those dealing with vector mechanics and dynamics, will benefit from this discussion.

influx
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Homework Statement


b98fa7.png


Homework Equations



RAO = b(Sinβj+Cosβk)

The Attempt at a Solution


[/B]
The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple product: A x (B x C) = (A•C)B - (A.B)C, but this isn't what they've done?

Thanks
 
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influx said:

Homework Statement


b98fa7.png


Homework Equations



RAO = b(Sinβj+Cosβk)

The Attempt at a Solution


[/B]
The box in red is ω. However I am unsure of where they got the box in blue from? As mentioned above, RAO = b(Sinβj+Cosβk) so not sure where they got the box in blue from? I know of the vector triple product: A x (B x C) = (A•C)B - (A.B)C, but this isn't what they've done?

Thanks

I would assume that they are doing the obvious thing, ie. calculating \mathbf{\omega} \times \mathbf{r}_{AO} first, and given the presence of a scalar factor of b (which goes missing in the second line before reappearing in the third) the vector in the blue box must therefore be \frac{\mathbf{\omega} \times \mathbf{r}_{AO}}{b}. (Although given that something did go missing partway through I would recommend double-checking this.)
 
Last edited:

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