Question

Si el vector u=(7,5,3) y v=(-3,q,0) encuentre el valor de q tal que |u+v|^2= 102

Answer 1

Veamos:

u + v = (7, 5, 3) + (- 3, q, 0) = (4, 5 + q, 3)

|u + v|^2 = 4^2 + (5 + q)^2 + 3^2 = 102

(5 + q)^2 = 102 - 16 - 9 = 77

(5 + q) = 8,78 ó - 8,78

q = 3,78; q = 13,78

Saludos Herminio

Corrijo: u + v = (2, 6 + q, 7)

|u + v|^2 = 4 + (6 + q)^2 + 49 = 102

(6 + q)^2 = 102 - 49 - 4 = 49

6 + q = 7; q = 1

6 + q = - 7; q = - 13