QCM14
\(\cos(\vec{u} , \vec{w}) = \frac{1}{\sqrt{10}}\)
Votre choixChoix attenduRéponse
On a \(\vec{u}(4 ; 0)\) et \(\vec{w}(1 ; -3)\).
\(\vec{u} . \vec{w} = 4 \times 1 + 0 \times (-3) = 4 + 0 = 4\)
\(||\vec{u}|| = \sqrt{4² + 0²} = 4\)
\(||\vec{w}|| = \sqrt{1² + 3²} = \sqrt{10}\)
\(\cos(\vec{u} , \vec{w}) = \frac{\vec{u} . \vec{w}}{||\vec{u}|| \times ||\vec{w}||} = \frac{4}{4\sqrt{10}} = \frac{1}{\sqrt{10}}\)