1. Determine how the following lines interact.
   1. (x, y, z) = (-2, 1, 3) + t(1, -1, 5);(x, y, z) = (-3, 0, 2) + s(-1, 2, -3)
   2. (x, y, z) = (1, 2, 0) + t(1, 1, -1);(x, y, z) = (3, 4, -1) + s(2, 2, -2)
   3. x = 2 + t, y = -1 + 2t, z = -1 - t;x = -1 - 2s, y = -1 -1s, z = 1 + s
   4. (x, y, z) = (1, -1, 2) + t(2, -1, 3);x = -3 - 4s, y = 1 + 2s, z = -4 -6s
2. Show that the two lines with equations(x, y, z) = (-1, 3, -4) + t(1, -1, 2) and(x, y, z) = (5, -3, 2) + s(-2, 2, 2)are perpendicular. Determine how the two lines interact.
3. Find the point of intersection of the line(x, y, z) = (1, -2, 1) + t(4, -3, -2)and the planex - 2y + 3z = -8.
4. Determine how the following lines and planes interact.
   1. (x, y, z) = (-1, 2, 3) + t(1, 2, 2);2x + 3y - 4z + 9 = 0.
   2. x = 2 - t, y = 3 - t, z = -1 + t;3x - y + 2z -1 = 0.
5. Determine the interaction of the line of intersection of the planesx + y - z = 1and3x + y + z = 3with the line of intersection of the planes2x - y + 2z = 4and2x + 2y + z = 1.
6. Determine the distance between the following points and lines:
   1. P(3, 7) and the line2x - 5y + 8 = 0.
   2. P(1, -5, 2) and the line(x, y, z) = (6, 0, 1) + t( 3, 1, 2).
7. The formula for the distance between any pointP(x₁, y₁, z₁)and any planeAx + By + Cz + D = 0is given by: Prove this formula is correct by using a similar method to find the distance between the point and a line in two dimensions.