Produto escalar: u = (1,−2,3) e v = (2,1,−1)

Sejam $\mathbf{u}=(1,-2,3)$ e $\mathbf{v}=(2,1,-1)$.

a) Calcule $\mathbf{u}\cdot \mathbf{v}$.

b) Calcule $\Vert \mathbf{u}\Vert$ e $\Vert \mathbf{v}\Vert$ e o cosseno do ângulo entre eles.

c) Os vetores são ortogonais? Justifique.

(a) $\mathbf{u}\cdot \mathbf{v}=1\cdot 2+(-2)\cdot 1+3\cdot (-1)=2-2-3=-3$.

(b) $\Vert \mathbf{u}\Vert =\sqrt{14}$, $\Vert \mathbf{v}\Vert =\sqrt{6}$, $\cos \theta =-3/(\sqrt{14}\sqrt{6})$…