Final answer:
To find the points of intersection between the curve r(t) and the paraboloid z, we equate the corresponding x, y, and z components and solve for t. Then we substitute the values of t back into the original equation to find the points.
Step-by-step explanation:
The curve r(t) = ti + (7t - t²)k intersects the paraboloid z = x² + y² at certain points. To find these points, we need to find the values of t that satisfy the equation
ti + (7t - t²)k = x² + y²
By equating the corresponding x, y, and z components, we can solve for t and substitute back into the original equation to find the points of intersection.