Question

Sabendo que |a|= 2√2, |b|= 4 e 45º o ângulo entre 'a' e 'b', calcule $|\frac{2}{5}a *\frac{1}{2}b|$

Answer 1

Produto escalar

$\large \boxed{\boxed{\mathsf{\vec{a}\cdot\vec{b}=|a|\cdot|b|\cdot\: cos(\theta)}}}$

$\boxed{\boxed{\mathsf{\vec{a}\cdot\vec{b}=2\sqrt{2}\cdot\,4\cdot\,cos(45^{\circ})}}}$

$\boxed{\boxed{\mathsf{\vec{a}\cdot\vec{b}=2\sqrt{2}\cdot\,4\cdot\dfrac{\sqrt{2}}{2}=4.2=8}}}$

$\mathsf{|\dfrac{2}{5}\vec{a}\cdot\dfrac{1}{2}\cdot\vec{b}|}\\\mathsf{|\dfrac{2}{5}\cdot\dfrac{1}{2}.8|=\dfrac{8}{5}}$

Verifique o gabarito.