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SciCode / 38.2 / Given three vectors, provide a function that returns the reciprocal vectors of…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

step background

Background For the input vectors

\overrightarrow{a_1}

\overrightarrow{a_2}

\overrightarrow{a_3}

, the reciprocal vectors are

$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot \left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_3}=2 \pi \frac{\overrightarrow{a_1} \times \overrightarrow{a_2}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$

Plain-text mathematical notation (without MathML)

Background

For the input vectors (a₁)→, (a₂)→, (a₃)→, the reciprocal vectors are

$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot \left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_3}=2 \pi \frac{\overrightarrow{a_1} \times \overrightarrow{a_2}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$

Original LaTeX notation

Background

For the input vectors $\overrightarrow{a_1}$, $\overrightarrow{a_2}$, $\overrightarrow{a_3}$, the reciprocal vectors are

$$
\begin{aligned}
& \overrightarrow{b_1}=2 \pi \frac{\overrightarrow{a_2} \times \overrightarrow{a_3}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_2}=2 \pi \frac{\overrightarrow{a_3} \times \overrightarrow{a_1}}{\overrightarrow{a_1} \cdot \left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)} \\
& \overrightarrow{b_3}=2 \pi \frac{\overrightarrow{a_1} \times \overrightarrow{a_2}}{\overrightarrow{a_1} \cdot\left(\overrightarrow{a_2} \times \overrightarrow{a_3}\right)}
\end{aligned}
$$

step description prompt

Given three vectors, provide a function that returns the reciprocal vectors of the input. The input is a list of three numpy arrays and the output should also be a list of three numpy arrays.

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Source and history

upstream_id / Original problem ID: 38.2
task_id: 0a601ee4-4479-5dad-ae40-88c776a4f49e
task_key: dev--96fdd33e-7a8f-5191-a8cf-e8ce0b324581--38~2e2
task_revision_id: 2
config / split: / dev

Official source

initial import