Hello, Jenny1

Show that the graph of: .r(t) .= .[f(t) - g(t)] i + [g(t) - h(t)]j +[h(t) - f(t)]k

lies on a plane passing through the origin.

We have these three parametric equations:

. . x .= .f(t) - g(t)

. . y .= .g(t) - h(t)

. . z .= .h(t) - f(t)

Add them and we get: .x + y + z.= .0

. . a plane which passes through the origin.