benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / There exist vectors a and b such that

Problem

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

problem

There exist vectors a\mathbf{a} and b\mathbf{b} such that \[\mathbf{a} + \mathbf{b} = \begin{pmatrix} 4 \\ 7 \end{pmatrix},\]where a\mathbf{a} is parallel to $\begin{pmatrix} 1 \\ 2 \end{pmatrix},$ and b\mathbf{b} is orthogonal to $\begin{pmatrix} 1 \\ 2 \end{pmatrix}.$ Find b.\mathbf{b}.
Plain-text mathematical notation (without MathML)
There exist vectors a and b such that
\[\mathbf{a} + \mathbf{b} = \begin{pmatrix} 4 \\ 7 \end{pmatrix},\]where a is parallel to $\begin{pmatrix} 1 \\ 2 \end{pmatrix},$ and b is orthogonal to $\begin{pmatrix} 1 \\ 2 \end{pmatrix}.$  Find b.
Original LaTeX notation
There exist vectors $\mathbf{a}$ and $\mathbf{b}$ such that
\[\mathbf{a} + \mathbf{b} = \begin{pmatrix} 4 \\ 7 \end{pmatrix},\]where $\mathbf{a}$ is parallel to $\begin{pmatrix} 1 \\ 2 \end{pmatrix},$ and $\mathbf{b}$ is orthogonal to $\begin{pmatrix} 1 \\ 2 \end{pmatrix}.$  Find $\mathbf{b}.$

level

Level 4

type

Precalculus

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
351dc561-88ef-5562-a560-2e72f590b600
task_key
precalculus--test--351dc561-88ef-5562-a560-2e72f590b600
task_revision_id
1
config / split
precalculus / test

Official source

initial import