Calcule el valor de K sabiendo que el modulo del vector V = (k,3) es 5
mafrov
Ambos valores de K son solución, puesto que un número negativo, elevado al cuadrado es positivo, por tanto ambos valores de k satisfacen el valor del modulo de V.
![\[\begin{gathered} {v_x} = k \hfill \\ {v_y} = 3 \hfill \\ \left| v \right| = 5 \hfill \\ \left| v \right| = \sqrt {{v_x}^2 + {v_y}^2} \hfill \\ 5 = \sqrt {{k^2} + {3^2}} \hfill \\ 25 = {k^2} + 9 \hfill \\ k = \pm \sqrt {25 - 9} \hfill \\ k = \pm \sqrt {16} \hfill \\ \left\{ \begin{gathered} {k_1} = 4 \hfill \\ {k_2} = - 4 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \]](https://tex.z-dn.net/?f=%5C%5B%5Cbegin%7Bgathered%7D%0A++%7Bv_x%7D+%3D+k+%5Chfill+%5C%5C%0A++%7Bv_y%7D+%3D+3+%5Chfill+%5C%5C%0A++%5Cleft%7C+v+%5Cright%7C+%3D+5+%5Chfill+%5C%5C%0A++%5Cleft%7C+v+%5Cright%7C+%3D+%5Csqrt+%7B%7Bv_x%7D%5E2+%2B+%7Bv_y%7D%5E2%7D++%5Chfill+%5C%5C%0A++5+%3D+%5Csqrt+%7B%7Bk%5E2%7D+%2B+%7B3%5E2%7D%7D++%5Chfill+%5C%5C%0A++25+%3D+%7Bk%5E2%7D+%2B+9+%5Chfill+%5C%5C%0A++k+%3D++%5Cpm+%5Csqrt+%7B25+-+9%7D++%5Chfill+%5C%5C%0A++k+%3D++%5Cpm+%5Csqrt+%7B16%7D++%5Chfill+%5C%5C%0A++%5Cleft%5C%7B+%5Cbegin%7Bgathered%7D%0A++%7Bk_1%7D+%3D+4+%5Chfill+%5C%5C%0A++%7Bk_2%7D+%3D++-+4+%5Chfill+%5C%5C+%0A%5Cend%7Bgathered%7D++%5Cright.+%5Chfill+%5C%5C+%0A%5Cend%7Bgathered%7D+%5C%5D "\[\begin{gathered} {v_x} = k \hfill \\ {v_y} = 3 \hfill \\ \left| v \right| = 5 \hfill \\ \left| v \right| = \sqrt {{v_x}^2 + {v_y}^2} \hfill \\ 5 = \sqrt {{k^2} + {3^2}} \hfill \\ 25 = {k^2} + 9 \hfill \\ k = \pm \sqrt {25 - 9} \hfill \\ k = \pm \sqrt {16} \hfill \\ \left\{ \begin{gathered} {k_1} = 4 \hfill \\ {k_2} = - 4 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered} \]")
1 votes
Thanks 0