Chapter 12.2, Problem 49ES

(a) Find the points where the curve $\text{r}=t\text{i}+t^2\text{j}-3t\text{k}$ intersects the plane $2x-y+z=-2.$

(b) For the curve and plane in part (a), find, to the nearest degree, the acute angle that the tangent line to the curve makes with a line normal to the plane at each point of intersection.