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MATH / Let a, b, and c be three unit vectors, such that the angle between any of them is the acute angle θ. The volume of the tetrahedron generated by these three vectors is (1)/(√(360)).…

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problem

Let a,\mathbf{a}, b,\mathbf{b}, and c\mathbf{c} be three unit vectors, such that the angle between any of them is the acute angle θ.\theta. The volume of the tetrahedron generated by these three vectors is 1360.\frac{1}{\sqrt{360}}. Find 3cos2θ−2cos3θ.3 \cos^2 \theta - 2 \cos^3 \theta.
Plain-text mathematical notation (without MathML)
Let a, b, and c be three unit vectors, such that the angle between any of them is the acute angle θ.  The volume of the tetrahedron generated by these three vectors is (1)/(√(360)).  Find
3cos²θ−2cos³θ.
Original LaTeX notation
Let $\mathbf{a},$ $\mathbf{b},$ and $\mathbf{c}$ be three unit vectors, such that the angle between any of them is the acute angle $\theta.$  The volume of the tetrahedron generated by these three vectors is $\frac{1}{\sqrt{360}}.$  Find
\[3 \cos^2 \theta - 2 \cos^3 \theta.\]

level

Level 5

type

Precalculus

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Source and history

task_id
954cc293-ae8f-5a12-8b8d-ad99a359ee1d
task_key
precalculus--test--954cc293-ae8f-5a12-8b8d-ad99a359ee1d
task_revision_id
1
config / split
precalculus / test

Official source

initial import