Päevaülesanne

Juhuslik

Harjutuskomplekt

Balti Tee 1991 · Ülesanne 17

Geomeetria

Let the coordinate planes have the reflection property. A beam falls onto one of them. How does the final direction of the beam after reflecting from all three coordinate planes depend on its initial direction?

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Ülevaade

Teemad

Koordinaadid ja vektorid · Ruumigeomeetria

Lahendused

Lahendus

Solution: Let the velocity vector of the beam be v⃗=(α,β,γ)\vec{v} = (\alpha, \beta, \gamma). Reflection from each of the coordinate planes changes the sign of exactly one of the coordinates α\alpha, β\beta and γ\gamma, and thus the final direction will be opposite to the initial one.