Perpendicular components of the perpendicular plane

In summary, the cross product of two acceleration vectors gives the perpendicular components of each in the perpendicular plane of "ar" and can be controlled by setting it equal to an angle in that plane. This can help explain the purpose of the cross product in understanding and manipulating vectors.
  • #1
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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  • #2
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.
 

1. What are perpendicular components of the perpendicular plane?

The perpendicular components of the perpendicular plane refer to the two lines that intersect at a right angle in a two-dimensional plane. These components are perpendicular to each other and form the basis of the perpendicular plane.

2. How are the perpendicular components of the perpendicular plane calculated?

The perpendicular components of the perpendicular plane can be calculated using the Pythagorean theorem. This involves finding the square root of the sum of the squares of the two components.

3. Why are perpendicular components of the perpendicular plane important in geometry?

The perpendicular components of the perpendicular plane are important in geometry because they help in understanding the relationship between different lines and angles in a two-dimensional plane. They also play a crucial role in various geometric proofs and constructions.

4. Can perpendicular components of the perpendicular plane exist in three-dimensional space?

No, perpendicular components of the perpendicular plane only exist in two-dimensional space. In three-dimensional space, there are three mutually perpendicular planes that intersect at a point, forming a three-dimensional coordinate system.

5. How can understanding perpendicular components of the perpendicular plane be applied in real life?

Understanding perpendicular components of the perpendicular plane can be applied in various fields such as architecture, engineering, and physics. It can help in designing and constructing structures, calculating forces and vectors, and analyzing geometric shapes and patterns.

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