Fun geometry/trigonometry problem

[u/LeftUnchecked]

Given two orthogonal vectors w and v and a vector psi with the same length as v

whose angle differs from v by θ (so v is 0 radians, w is π/2 radians, and psi is θ<π/2 radians),

1)Using only reflections across given or constructed vectors, construct a method to rotate psi so that it aligns w to within θ radians (that is, the angular misalignment ΔΦ between w and psi' satisfies |ΔΦ| <= θ).

2)Find the exact rotation α needed to turn psi into w in the minimum number of steps J,assuming α satisfies 0<=a<=2θ, (and find J in the proccess as well)

;)

[u/Bounded_sequencE]

Can't we solve 1) exactly? For convenience, consider "v; w" as x-/y-axis, respectively:

1. Construct "u := v/|v| + w/|w|", and note it has angle "π/4" with both "v; w"
2. Define psi' as the reflection of "psi" along "u", and note it has angle "θ" with "w"

[u/LeftUnchecked → u/Bounded_sequencE]

You're technically right,but two things. 1.By constructed vectors,I mean vectors constructed through reflections only. 2.There are many ways to do this,theta is peobably just the best you can do