Reflections in R3

[rico]

In this problem, we study a special reflection in R3. Let L be a line in R3. A geometric transformation of R3 is called a reflection across L if it leaves the points on L invariant and maps a point P which is not on L to the point P′ such that the midpoint of the line segment PP′ is on L and the line segment PP′ is orthogonal to L.

Find the 3×3 matrix F of the reflection across the diagonal of the first octant in R3. That is, find the 3×3 matrix F which has the property that for every v ∈ R3 the head of the vector Fv is the reflection of the head of the vector v across the diagonal of the first octant.

I don't really know how to go about starting this problem, I think I need to create vectors with values in spherical coordinates but I am not sure that is the correct way to go about it.

 

[Steven G]

You need to try something. After that please share your work with us so we can help. It really is hard to help you w/o seeing what you have done.

 

[Cubist]

... I think I need to create vectors with values in spherical coordinates but I am not sure that is the correct way to go about it.

OP - can you tell us more about your thinking? Is there a simpler way that you can describe the transform in the first paragraph?

 

[rico]

I was able to figure it out, thank you!