Question

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

Answer 1

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)