Dados los puntos A( - 1, 3), B(2, 7), C(0, - 2), calcula : - Un vector paralelo a CA de moódulo 10 - Un vector perpendicular a CA de módulo 10 - Un vector ortonormal a CA?

CA = ( - 1, 5)

1) X || AC→ X = kAC = ( - k, 5k)

||X|| = k ||AC|| = k√26 = 10→ k = 10 / √26

X = ( - 10 / √26 ; 50 / √26)

ó

X = (10 / √26 ; - 50 / √26)

2) X⊥ CA → X·CA = 0

X = (a, b)→ (a, b)·( - 1, 5) = 0 - a + 5b = 0→ a = 5b

||X||² = 100→ a² + b² = 100

(5b)² + b² = 100

|b| = 10 / √26→ |a| = 50 / √26

X = (50 / √26, 10 / √26) ó X = ( - 50 / √26, - 10 / √26).