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Home » L'entreprise peut produire 4 gadgets A et 2 gadgets B. - RTA

L'entreprise peut produire 4 gadgets A et 2 gadgets B. - RTA

📅 May 11, 2026 👤 scraface

May 11, 2026

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📌 A software engineer renders light reflection in an AR app using the law of reflection: angle of incidence = angle of reflection. A ray hits a surface at point $(3, 4)$ with direction vector $\langle -1, 2

📌 angle$. What is the slope of the reflected ray relative to the line $y = 0$?

📌 First, find the normal vector. The surface is horizontal (assumed), so the normal is vertical: $\langle 0, 1

📌 Incident direction: $ec{i} = \langle -1, 2

📌 Unit normal: $ ec{n} = \langle 0, 1

📌 Angle between $ec{i}$ and $ec{n}$ gives reflection. Use vector reflection formula:

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\vec{w} = \begin{pmatrix} 2 \cdot 3 \\ 2 \cdot (-1) \\ 2 \cdot 2 \end{...
Subtract the vectors component-wise:
\vec{w} = \begin{pmatrix} 6 - (-6) \\ -2 - 12 \\ 4 - 3 \end{pmatrix} =...
Thus, the vector $\vec{w}$ is:
\boxed{\begin{pmatrix} 12 \\ -14 \\ 1 \end{pmatrix}}
Question: A hydrologist models the flow of groundwater in a 3D aquifer...
Let the point on the line be $\vec{r}(t) = \begin{pmatrix} 1 + 2t \\ t...
Let $P = (3, -1, 2)$. The vector from the point on the line to $P$ is:
\vec{d}(t) = \vec{P} - \vec{r}(t) = \begin{pmatrix} 3 - (1 + 2t) \\ -1...
To find the closest point, minimize the magnitude of $\vec{d}(t)$, or...

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