Perpendicular components of the perpendicular plane

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SUMMARY

The discussion focuses on the mathematical concept of the cross product of two acceleration vectors, specifically how it yields the perpendicular components of each vector. The equations provided demonstrate that the cross product, represented as (a cross ar), results in a vector ap that lies in the perpendicular plane of ar. The discussion emphasizes the importance of understanding the orientation of the vectors and the implications of setting the cross product equal to an angle in the perpendicular plane.

PREREQUISITES
  • Understanding of vector mathematics, specifically cross products.
  • Familiarity with acceleration vectors represented in component form.
  • Knowledge of three-dimensional coordinate systems.
  • Basic grasp of vector operations and their geometric interpretations.
NEXT STEPS
  • Study the properties of cross products in vector calculus.
  • Explore applications of cross products in physics, particularly in mechanics.
  • Learn about the geometric interpretation of vectors in three-dimensional space.
  • Investigate the role of angles in vector operations and their implications in motion dynamics.
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Students and professionals in physics, engineering, and mathematics who are working with vector analysis and dynamics, particularly those interested in the behavior of acceleration vectors in three-dimensional space.

Philosophaie
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What does the the cross product of two acceleration vectors do?

(a cross ar) = 0

where a =axi + ayj + azk and ar = arxi + aryj + arzk

(a cross ar)x = ay*arz - az*ary
(a cross ar)y = az*arx - ax*arz
(a cross ar)z = ax*ary - ay*arx

It gives the perpendicular components of each.

In the perpendicular plane of "ar" what happens if you set the the cross product equal to an angle on that perpendicular plane.

To give you control of which way the "ar" will execute:

(a cross ar) = ap where ap = apxi +apyj + apzk

ap is in the perpendicular plane of ar.
 
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Philosophaie said:
What does the the cross product of two acceleration vectors do?

(a cross ar) = 0

where a =axi + ayj + azk and ar = arxi + aryj + arzk

(a cross ar)x = ay*arz - az*ary
(a cross ar)y = az*arx - ax*arz
(a cross ar)z = ax*ary - ay*arx

It gives the perpendicular components of each.
In the perpendicular plane of "ar" what happens if you set the the cross product equal to an angle on that perpendicular plane.


To give you control of which way the "ar" will execute:

(a cross ar) = ap where ap = apxi +apyj + apzk

ap is in the perpendicular plane of ar.

What are you doing ? What's r ? Your question is vague and I cannot understand it. What do you mean by perpendicular plane ? Perpendicular to what ? A plane is a plane made of two independent coordinates ! Can you explain what are you doing exactly ?

I think I gave you the reason why no one replied to your thread.
 

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