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MATH / Let v₁, v₂, …, v_(k) be unit vectors such that mathbf{v}_1 + mathbf{v}_2 + dots + mathbf{v}_k = begin{pmatrix} 6 -5 end{pmatrix}.Find the smallest possible value of k. Note: A uni…

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problem

Let v1,\mathbf{v}_1, v2,\mathbf{v}_2, …,\dots, vk\mathbf{v}_k be unit vectors such that \[\mathbf{v}_1 + \mathbf{v}_2 + \dots + \mathbf{v}_k = \begin{pmatrix} 6 \\ -5 \end{pmatrix}.\]Find the smallest possible value of k.k. Note: A unit vector is a vector of magnitude 1.
Plain-text mathematical notation (without MathML)
Let v₁, v₂, …, v_(k) be unit vectors such that
\[\mathbf{v}_1 + \mathbf{v}_2 + \dots + \mathbf{v}_k = \begin{pmatrix} 6 \\ -5 \end{pmatrix}.\]Find the smallest possible value of k.

Note: A unit vector is a vector of magnitude 1.
Original LaTeX notation
Let $\mathbf{v}_1,$ $\mathbf{v}_2,$ $\dots,$ $\mathbf{v}_k$ be unit vectors such that
\[\mathbf{v}_1 + \mathbf{v}_2 + \dots + \mathbf{v}_k = \begin{pmatrix} 6 \\ -5 \end{pmatrix}.\]Find the smallest possible value of $k.$

Note: A unit vector is a vector of magnitude 1.

level

Level 4

type

Precalculus

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Source and history

task_id
fc4e8fb1-b3ce-5c72-8d58-f044b2ef0890
task_key
precalculus--test--fc4e8fb1-b3ce-5c72-8d58-f044b2ef0890
task_revision_id
1
config / split
precalculus / test

Official source

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