Decide a matrix for a vector that goes through various morphs

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Homework Help Overview

The discussion revolves around determining a matrix for a vector that undergoes various transformations, specifically focusing on rotation and reflection in a 3D coordinate system.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore different matrix setups for rotation and reflection, questioning the definitions and setups of the XYZ axes. There is discussion about the distinction between reflection and projection, as well as the implications of the rotation direction.

Discussion Status

Some participants have offered insights into the nature of reflections and the need to clarify the setup of the coordinate system. There is an ongoing exploration of different options for the reflection matrix, with some participants attempting to visualize the transformations involved.

Contextual Notes

There is a lack of explicit information regarding the specific setup of the XYZ axes, which is affecting the interpretation of the reflection matrix. Additionally, the problem does not specify the exact nature of the mirroring required.

Wi_N
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Homework Statement
1. first a quarter rotation on the x-axis. 2. then being mirrored on xy-plane. 3. Then projected on the plane x+ 2y+ 3z= 0.
Relevant Equations
$$\begin{pmatrix}
1 & 0 & 0 \\
0 & cos(\theta) & -sin(\theta) \\
0& sin(\theta) & cos(\theta)
\end{pmatrix}$$

for rotating on the x-axis.
vector=(abc)

1.
$$\begin{pmatrix}
1 & 0 & 0 \\
0 & cos(\theta) & -sin(\theta) \\
0& sin(\theta) & cos(\theta)
\end{pmatrix}$$
The rotation part is correct.

2.
$$\begin{pmatrix}
1 & 0 & 0 \\
0 & 1 & 0 \\
0& 0 & 0
\end{pmatrix}$$ is wrong apparently

how do I do the mirroring?

step 3 i can do just fine.
 
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Different authors use different setups for the XYZ setup. Do you know which one the author uses? Your matrix sends ##(x,y,z)## to ##(x, y,0)## which is not a reflection but a projection. In 2D, if you reflect across the y axis, you send ##(x,y)## to ##(-x,y)##. But the reflection you have will depend on how ##XYZ## axes are setup.
 
WWGD said:
Different authors use different setups for the XYZ setup. Do you know which one the author uses? Your matrix sends ##(x,y,z)## to ##(x, y,0)## which is not a reflection but a projection. In 2D, if you reflect across the y axis, you send ##(x,y)## to ##(-x,y)##. But the reflection you have will depend on how ##XYZ## axes are setup.
it doesn't specify just that it mirrors.
 
Wi_N said:
it doesn't specify just that it mirrors.
Then it seems you just have to try different options.
 
WWGD said:
Then it seems you just have to try different options.

could you give one example? it said the rotation was in positive direction, does that help?
 
Can you see what happens when you reflect a generic (x,y,z) along either of the 3 planes? This should help you define the reflection matrix. Does it help?
 
WWGD said:
Can you see what happens when you reflect a generic (x,y,z) along either of the 3 planes? This should help you define the reflection matrix. Does it help?
not really.
 
Ok, let's see if this works:
Draw a horizontal line L . At any point of L draw a perpendicular line segment S to L so that the endpoints of S are both equidistant to L. The endpoints of S are a point and its reflection about a plane. Can you tell the relation between the two emdpoints of S ( in coordinates)?

If not, maybe @BvU can help illustrate it better?
 
Last edited:
ok so a reflecton in xy plane is given by

100
010
00-1
 
  • #10
is this correct?
 
  • #11
Yes, that is correct.
 
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