7. Consider the planes $-x + 2y + z = 1$ and $x + y + z = 0$. They intersect along a straight line. Determine a vector equation for their intersection.
8. Consider the plane $3x + 2y - 4z = -3$ and the straight line with equation $r(t) = (-2t + 5, 3t - 5, 4t - 6)$.
a. Determine whether the line and the plane intersect. If they do, then find their point of intersection
b. Determine whether the point $(0, -1, 3)$ belongs to the plane or not.
c. Determine whether the point $(3, -2, -1)$ belongs to the line or not.
d. Determine whether the given line intersects with the line with equation $l(t) = (3t + 4, -8t, -3t - 7)$.