Describe the curve defined by the vector function r(t) = (4

Last updated: 7/4/2022

Describe the curve defined by the vector function r(t) = (4 + t, 1 + 3t, -4 + 5t). Solution The corresponding parametric equations are x=___, y = 1 + 3t, z =____ which we recognize from the equations x = xo + at, y = Yo + bt, z = Zo + ct as parametric equations of a line passing through the point (4, 1, -4) and parallel to the vector (1, 3, 5). Alternatively, we could observe that the function can be written as r = ro + tv, where ro = (4, 1, -4) and v =_______ and this is the vector equation of a line as given by the equation r=ro + tv.