determine ft so that the curve Xt3tt2ft lies in a planeSolut

determine f(t) so that the curve X(t)=(3t,t^2,f(t) lies in a plane

Solution

the equation of the plane is x/a+y/b+z/c=1

given X(t)=(3t,t^2,f(t))

=>3t/a+t²/b+f(t)/c=1

=>f(t)/c=-3t/a-t²/b+1

=>f(t)=c(-3t/a-t²/b+1)

=>f(t)=(-3c/a)t+(-c/b)t²+c

=>f(t)=a1t²+a2t+c