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MATH / For certain vectors p and q, the vectors 3p+q and 5p−3q are orthogonal. Also, the vectors 2p+q and 4p−2q are orthogonal. If θ is the angle between p and q, then find cosθ.

Problem

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problem

For certain vectors p\mathbf{p} and q,\mathbf{q}, the vectors 3p+q3 \mathbf{p} + \mathbf{q} and 5p−3q5 \mathbf{p} - 3 \mathbf{q} are orthogonal. Also, the vectors 2p+q2 \mathbf{p} + \mathbf{q} and 4p−2q4 \mathbf{p} - 2 \mathbf{q} are orthogonal. If θ\theta is the angle between p\mathbf{p} and q,\mathbf{q}, then find cosθ.\cos \theta.
Plain-text mathematical notation (without MathML)
For certain vectors p and q, the vectors 3p+q and 5p−3q are orthogonal.  Also, the vectors 2p+q and 4p−2q are orthogonal.  If θ is the angle between p and q, then find cosθ.
Original LaTeX notation
For certain vectors $\mathbf{p}$ and $\mathbf{q},$ the vectors $3 \mathbf{p} + \mathbf{q}$ and $5 \mathbf{p} - 3 \mathbf{q}$ are orthogonal.  Also, the vectors $2 \mathbf{p} + \mathbf{q}$ and $4 \mathbf{p} - 2 \mathbf{q}$ are orthogonal.  If $\theta$ is the angle between $\mathbf{p}$ and $\mathbf{q},$ then find $\cos \theta.$

level

Level 5

type

Precalculus

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Source and history

task_id
396356fc-b189-5439-a447-0b054cf98f37
task_key
precalculus--test--396356fc-b189-5439-a447-0b054cf98f37
task_revision_id
1
config / split
precalculus / test

Official source

initial import