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MATH / One line is defined by

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problem

One line is defined by \[\begin{pmatrix} 3 \\ -10 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ -9 \\ -2 \end{pmatrix}.\]Another line is defined by \[\begin{pmatrix} -5 \\ -3 \\ 6 \end{pmatrix} + u \begin{pmatrix} 4 \\ -18 \\ -4 \end{pmatrix}.\]These two lines are parallel. Find the distance between these two lines.
Plain-text mathematical notation (without MathML)
One line is defined by
\[\begin{pmatrix} 3 \\ -10 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ -9 \\ -2 \end{pmatrix}.\]Another line is defined by
\[\begin{pmatrix} -5 \\ -3 \\ 6 \end{pmatrix} + u \begin{pmatrix} 4 \\ -18 \\ -4 \end{pmatrix}.\]These two lines are parallel.  Find the distance between these two lines.
Original LaTeX notation
One line is defined by
\[\begin{pmatrix} 3 \\ -10 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ -9 \\ -2 \end{pmatrix}.\]Another line is defined by
\[\begin{pmatrix} -5 \\ -3 \\ 6 \end{pmatrix} + u \begin{pmatrix} 4 \\ -18 \\ -4 \end{pmatrix}.\]These two lines are parallel.  Find the distance between these two lines.

level

Level 5

type

Precalculus

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Source and history

task_id
74c3e212-8c29-5da8-ad0e-4bc2d2132152
task_key
precalculus--test--74c3e212-8c29-5da8-ad0e-4bc2d2132152
task_revision_id
1
config / split
precalculus / test

Official source

initial import