Question

Achar um vetor x de modulo igual a 5 de mesmo sentido que o vetor v= 6i-2j-3k.Me ajudem por favor!!!

Answer 1

Bom dia

x = (x1, x2, x3)
v = (6, -2, -3)

lxl = x1² + x2² + x3² = 5

x1² + x2² + x3² = 25

x1/6 = -x2/2 = -x3/3 

x2 = -2x1/6 = -x1/3
x3 = -3x1/6 = -x1/2 

x1² + x1²/9 + x1²/4 = 25  

49x1²/36 = 25
x1²  = 36*25/49
x1²  = 6*5/7 = 30/7

x1/6 = -x2/2 = -x3/3 

30/42 = -x2/2 = -x3/3 

x2 = -60/42 = -10/7
x3 = -90/42 = -15/7 

o vetor x = (30/7, -10/7, -15/7)