Question

At what points does the curve R(t)=ti + (4t-t^2)k intersect the paraboloid z=x^2+3y^2?

Answer 1

This is what i have done: \[z= \cos^2s+3\sin^2s\]

Answer 2

\[3\sin^2s=0 \implies s=0,\pi\]

Answer 3

setting components equal... I think im missing something....

Answer 4

r is a vector function

Answer 5

my problem occurs, the proof that im doing it wrong is when i get to: \[\cos^2s + 3\sin^2s=4t-t^2 \] the way i solved for s and t i get\[3=1\]