Question

dado o vetor V = (-1,-2), achar o vetor paralelo a V que tenha o mesmo sentido de V e módulo quatro.

Answer 1

O vetor procurado é

$\overrightarrow{\mathbf{w}}=\dfrac{4\overrightarrow{\mathbf{v}}}{\|\overrightarrow{\mathbf{v}}\|}\\\\\\ \overrightarrow{\mathbf{w}}=\dfrac{4\cdot (-1,\;-2)}{\|(-1,\;-2)\|}\\\\\\ \overrightarrow{\mathbf{w}}=\dfrac{(4\cdot (-1),\;4\cdot (-2))}{\sqrt{(-1)^{2}+(-2)^{2}}}\\\\\\ \overrightarrow{\mathbf{w}}=\dfrac{(-4,\;-8)}{\sqrt{1+4}}\\\\\\ \overrightarrow{\mathbf{w}}=\dfrac{(-4,\;-8)}{\sqrt{5}}\\\\\\ \boxed{\begin{array}{c}\overrightarrow{\mathbf{w}}=\left(-\,\dfrac{4}{\sqrt{5}},\;-\,\dfrac{8}{\sqrt {5}}\right ) \end{array}}$