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MATH / A plane contains the vector begin{pmatrix} 1 2 3 end{pmatrix} and has normal vector begin{pmatrix} 4 5 6 end{pmatrix}. A line contains the vector …

Problem

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problem

A plane contains the vector $\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and has normal vector $\begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}.$ A line contains the vector $\begin{pmatrix} -1 \\ 0 \\ 5 \end{pmatrix}$ and has direction vector $\begin{pmatrix} -1 \\ -1 \\ 2 \end{pmatrix}.$ Find the point of intersection of the plane and line.
Plain-text mathematical notation (without MathML)
A plane contains the vector $\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and has normal vector $\begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}.$  A line contains the vector $\begin{pmatrix} -1 \\ 0 \\ 5 \end{pmatrix}$ and has direction vector $\begin{pmatrix} -1 \\ -1 \\ 2 \end{pmatrix}.$  Find the point of intersection of the plane and line.
Original LaTeX notation
A plane contains the vector $\begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix}$ and has normal vector $\begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}.$  A line contains the vector $\begin{pmatrix} -1 \\ 0 \\ 5 \end{pmatrix}$ and has direction vector $\begin{pmatrix} -1 \\ -1 \\ 2 \end{pmatrix}.$  Find the point of intersection of the plane and line.

level

Level 4

type

Precalculus

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Source and history

task_id
0ad049cc-044c-5531-ad50-9de02a7d3d3d
task_key
precalculus--test--0ad049cc-044c-5531-ad50-9de02a7d3d3d
task_revision_id
1
config / split
precalculus / test

Official source

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