How to show x1/y1=x2/y2=x3/y3?

Question

Let P₁=(x₁, x_2, x₃) and P₂=(y₁, y_2, y₃) be two vectors. If P₁ is parallel to P₂, show that x₁/y₁=x₂/y₂=x₃/y₃.

Answer 1

Then P2 = k*P1, because they are scalar multiples of each other if they are parallel.

(y1,y2,y3) = (k*x1, k*x2, K*x3)

y1 = k*x1

y2 = k*x2

y3 = k*x3

Then

x1/y1 = x2/y2 = x3/y3 = 1/k