Final answer:
The line passing through points P(1, 0, 6) and Q(7, -1, 7) intersects the plane x + y - 2 = 7 at point Q(7, -1, 7), which is derived through parametric equations and solving for the parameter t.
Step-by-step explanation:
The question asks to find the point of intersection between a line passing through points P(1, 0, 6) and Q(7, -1, 7) with the plane represented by the equation x + y - 2 = 7. To solve this, we first need to find the parametric equations of the line by using the two given points P and Q to define the direction vector Δ(x, y, z), which will be (6, -1, 1) subtracting coordinates of P from Q. The parametric equations of the line are:
- x = 1 + 6t
- y = -t
- z = 6 + t
Next, we substitute these into the equation of the plane x + y - 2 = 7 to find the value of parameter t:
1 + 6t - t - 2 = 7
Solving the above equation for t gives us t = 1. Plugging t back into the parametric equations, we get the intersection point (7, -1, 7), which is actually point Q itself. Therefore, the line intersects the plane at point Q.