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MATH / There are an infinite number of vectors v such that

Problem

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problem

There are an infinite number of vectors v\mathbf{v} such that \[\begin{pmatrix} 1 \\ 2 \\ -5 \end{pmatrix} \times \mathbf{v} = \begin{pmatrix} 90 \\ 30 \\ 30 \end{pmatrix}.\]Find the vector v\mathbf{v} that has the smallest magnitude.
Plain-text mathematical notation (without MathML)
There are an infinite number of vectors v such that
\[\begin{pmatrix} 1 \\ 2 \\ -5 \end{pmatrix} \times \mathbf{v} = \begin{pmatrix} 90 \\ 30 \\ 30 \end{pmatrix}.\]Find the vector v that has the smallest magnitude.
Original LaTeX notation
There are an infinite number of vectors $\mathbf{v}$ such that
\[\begin{pmatrix} 1 \\ 2 \\ -5 \end{pmatrix} \times \mathbf{v} = \begin{pmatrix} 90 \\ 30 \\ 30 \end{pmatrix}.\]Find the vector $\mathbf{v}$ that has the smallest magnitude.

level

Level 4

type

Precalculus

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Source and history

task_id
170b8775-cde5-5a7d-880b-28a73a0ce2b0
task_key
precalculus--test--170b8775-cde5-5a7d-880b-28a73a0ce2b0
task_revision_id
1
config / split
precalculus / test

Official source

initial import