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MATH / Let a and b be orthogonal vectors. If operatorname{proj}_{mathbf{a}} begin{pmatrix} 0 13 end{pmatrix} = begin{pmatrix} 6 4 end{pmatrix}, then find …

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problem

Let a\mathbf{a} and b\mathbf{b} be orthogonal vectors. If $\operatorname{proj}_{\mathbf{a}} \begin{pmatrix} 0 \\ 13 \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \end{pmatrix},$ then find $\operatorname{proj}_{\mathbf{b}} \begin{pmatrix} 0 \\ 13 \end{pmatrix}.$
Plain-text mathematical notation (without MathML)
Let a and b be orthogonal vectors.  If $\operatorname{proj}_{\mathbf{a}} \begin{pmatrix} 0 \\ 13 \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \end{pmatrix},$ then find $\operatorname{proj}_{\mathbf{b}} \begin{pmatrix} 0 \\ 13 \end{pmatrix}.$
Original LaTeX notation
Let $\mathbf{a}$ and $\mathbf{b}$ be orthogonal vectors.  If $\operatorname{proj}_{\mathbf{a}} \begin{pmatrix} 0 \\ 13 \end{pmatrix} = \begin{pmatrix} 6 \\ 4 \end{pmatrix},$ then find $\operatorname{proj}_{\mathbf{b}} \begin{pmatrix} 0 \\ 13 \end{pmatrix}.$

level

Level 5

type

Precalculus

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Source and history

task_id
b9b03a2e-e687-5bac-9360-b8d4bdcdf945
task_key
precalculus--test--b9b03a2e-e687-5bac-9360-b8d4bdcdf945
task_revision_id
1
config / split
precalculus / test

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