Question

Calcula los vectores unitarios, de cada uno de los vectores que se presentan a continuación. 8. u = (5, 2) 9. v = (6, 4) 10. w = (7, -2)

Answer 1

PREGUNTA

Calcula los vectores unitarios, de cada uno de los vectores que se presentan a continuación.  

8. u = (5, 2)  

9. v = (6, 4)

10. w = (7, -2)

SOLUCIÓN

Hola!! :D

Recuerda que un vector unitario(u) de un vector A está dado por:

                             $\boxed{\boldsymbol{\mathrm{\hat{u} = \dfrac{\overrightarrow{A}}{|\overrightarrow{A}|}}}}\\\\Donde\\\\\overrightarrow{A}: \mathrm{Vector \: A}\\\\|\overrightarrow{A}|: \mathrm{M\'odulo \: del \: vector\:A}$

Entonces

                    $\boldsymbol{8. \: \overrightarrow{u} = (5,2)}\\\\|\overrightarrow{u}| = \sqrt{5^2+2^2} = \sqrt{29}\\\\\mathrm{El \:vector \:unitario \: es:}\\\\\hat{u} = \dfrac{\overrightarrow{u}}{|\overrightarrow{u}|} \\\\\\\hat{u} = \dfrac{(5,2)}{\sqrt{29}}\\\\\\\boldsymbol{\boxed{\mathrm{\hat{u} = (\dfrac{5}{\sqrt{29}},\dfrac{2}{\sqrt{29}})}}}$

                    $\boldsymbol{9. \: \overrightarrow{v} = (6,4)}\\\\|\overrightarrow{v}| = \sqrt{6^2+4^2} = 2\sqrt{13}\\\\\mathrm{El \:vector \:unitario \: es:}\\\\\hat{u} = \dfrac{\overrightarrow{v}}{|\overrightarrow{v}|} \\\\\\\hat{u} = \dfrac{(6,4)}{2\sqrt{13}}\\\\\\\boldsymbol{\boxed{\mathrm{\hat{u} = (\dfrac{3}{\sqrt{13}},\dfrac{2}{\sqrt{13}})}}}$

                    $\boldsymbol{10. \: \overrightarrow{w} = (7,-2)}\\\\|\overrightarrow{w}| = \sqrt{7^2+(-2)^2} = \sqrt{53}\\\\\mathrm{El \:vector \:unitario \: es:}\\\\\hat{u} = \dfrac{\overrightarrow{w}}{|\overrightarrow{w}|} \\\\\\\hat{u} = \dfrac{(7,-2)}{\sqrt{53}}\\\\\\\boldsymbol{\boxed{\mathrm{\hat{u} = (\dfrac{7}{\sqrt{53}},\dfrac{-2}{\sqrt{53}})}}}$