Final answer:
To find the point of intersection, substitute x, y, and z values from the line equation into the plane equation and solve for t.
Step-by-step explanation:
To find the point at which the line intersects the given plane, we need to determine the value of t that satisfies the equation of the plane. Given the equation of the line x = 2 - 2t, y = 3t, z = 1/t and the equation of the plane x²y - z = 4, we substitute the values of x, y, and z from the line equation into the plane equation.
By substituting the values of x, y, and z into the plane equation, we get (2 - 2t)²(3t) - 1/t = 4. Simplifying this equation and solving for t will give us the value of t at which the line intersects the plane.
We can then substitute the value of t back into the line equation to find the coordinates of the point at which the line intersects the plane.