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MATH / Let u and v be vectors such that ‖u‖=‖v‖=2 and u⋅v=−1. If θ is the angle between the vectors u+v and 2u−v, then find cosθ.

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problem

Let u\mathbf{u} and v\mathbf{v} be vectors such that ‖u‖=‖v‖=2\|\mathbf{u}\| = \|\mathbf{v}\| = 2 and u⋅v=−1.\mathbf{u} \cdot \mathbf{v} = -1. If θ\theta is the angle between the vectors u+v\mathbf{u} + \mathbf{v} and 2u−v,2 \mathbf{u} - \mathbf{v}, then find cosθ.\cos \theta.
Plain-text mathematical notation (without MathML)
Let u and v be vectors such that ‖u‖=‖v‖=2 and u⋅v=−1.  If θ is the angle between the vectors u+v and 2u−v, then find cosθ.
Original LaTeX notation
Let $\mathbf{u}$ and $\mathbf{v}$ be vectors such that $\|\mathbf{u}\| = \|\mathbf{v}\| = 2$ and $\mathbf{u} \cdot \mathbf{v} = -1.$  If $\theta$ is the angle between the vectors $\mathbf{u} + \mathbf{v}$ and $2 \mathbf{u} - \mathbf{v},$ then find $\cos \theta.$

level

Level 5

type

Precalculus

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Source and history

task_id
42db5c9e-4d3f-50f6-a22a-4773926aed24
task_key
precalculus--test--42db5c9e-4d3f-50f6-a22a-4773926aed24
task_revision_id
1
config / split
precalculus / test

Official source

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