Alternate meaningful version: Given fixed vectors $ \mathbf{w} = \langle 1, 0, 1 \rangle $, $ \mathbf{u} = \langle 0, 1, 2 \rangle $, and a unit vector $ \mathbf{v} $, find the maximum value of $ \left| \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) \right| $, which measures projection onto the binormal vector.

February 22, 2026

$Alternate meaningful version: Given fixed vectors $ \mathbf{w} = \langle 1, 0, 1 \rangle $, $ \mathbf{u} = \langle 0, 1, 2 \rangle $, and a unit vector $ \mathbf{v} $, find the maximum value of $ \left| \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) \right| $, which measures projection onto the binormal vector.$

5Question: Let $ \mathbf{v} $ be a vector in $ \mathbb{R}^3 $ such that $ \|\mathbf{v}\| = 1 $ and $ \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) = \frac{1}{2} $, where $ \mathbf{w} = \langle 1, 0, 1 \rangle $, $ \mathbf{u} = \langle 0, 1, 2 \rangle $. Find the maximum possible value of $ \|\mathbf{v}\| $ under the constraint—wait, correction: $ \|\mathbf{v}\| $ is fixed at 1, so instead reinterpret: find the maximum of $ \|\mathbf{v}\|^2 $ given the dot product condition, b
Wait—reformulate properly.
Corrected interpretation: Find the maximum value of $ k $ such that $ \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) = \frac{1}{2} $ is possible for a unit vector $ \mathbf{v} $, or equivalently find the maximum efficiency of such a dot product under normalization. But since $ \|\mathbf{v}\| $ is constrained to 1, the equation defines a constraint; perhaps instead ask: find the maximum possible value of $ \left| \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) \right| $ over all unit v
And since $ \|\mathbf{v}\| = 1 $, the maximum of the absolute value is $ \|\mathbf{w} \times \mathbf{u}\| $.
\mathbf{w} \times \mathbf{u} = \begin{vmatrix}
& 0 & 1 \\

Related Articles

Trending Articles