Final answer:
To find the point of intersection between the line x=1+t, y=2t, z=-3t and the plane x + y + z = -5, substitute the values of x, y, and z from the line equations into the plane equation to solve for t. The point of intersection is P(0, -2, 3), which means x = 0, y = -2, and z = 3.
Step-by-step explanation:
To find the point of intersection between the line and the plane, we need to equate the coordinates of the line with the equation of the plane.
Given that the line is represented by the equations x=1+t, y=2t, and z=-3t, and the plane is represented by the equation x+y+z=-5, we can substitute the values of x, y, and z from the line equations into the plane equation to solve for t.
Solving the equation, we get t = -1. Substituting this value back into the line equations, we find that the point of intersection is P(0, -2, 3).