Decide a matrix for a vector that goes through various morphs

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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.
 

Discussion

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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.
 
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?
 
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