benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / One line is parameterized by

Problem

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

problem

One line is parameterized by \[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by \[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at P.P. If θ\theta is the acute angle formed by the two lines at P,P, then find cosθ.\cos \theta.
Plain-text mathematical notation (without MathML)
One line is parameterized by
\[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by
\[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at P.  If θ is the acute angle formed by the two lines at P, then find cosθ.
Original LaTeX notation
One line is parameterized by
\[\begin{pmatrix} 2 - 3t \\ -5 - 2t \\ 1 - 6t \end{pmatrix}.\]Another line is parameterized by
\[\begin{pmatrix} -\frac{3}{2} + s \\ 2s \\ -6 + 2s \end{pmatrix}.\]The two lines intersect at $P.$  If $\theta$ is the acute angle formed by the two lines at $P,$ then find $\cos \theta.$

level

Level 5

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
4cf6a34e-9870-552e-b5a2-af0d77f04c64
task_key
precalculus--test--4cf6a34e-9870-552e-b5a2-af0d77f04c64
task_revision_id
1
config / split
precalculus / test

Official source

initial import