Doubble integrals

Question

Suppose F (x,y)=(6x−y)i +(x) j . (a) Find a vector parametric equation for the line segment from the origin to the point (4,16) using t as a parameter. r(t)=?

Answer 1

We have two points: (0,0) and (4,16) and need a straight line segment equation. The form is obtained like following:

r(t) = (0, 0) + t (4-0, 16-0) = (0,0) + (4t, 16t) = (4t, 16t). 0 «t «1