Thread: parametric equation

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.

Thank you very much.

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.