1. Determine how the following lines interact. a. (x, y, z) = (-2, 1, 3) +...

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1. Determine how the following lines interact. a. (x, y, z) = (-2, 1, 3) + t(1, -1, 5); (x, y, z) = (-3, 0, 2) + s(-1, 2, -3) b. (x, y, z) = (1, 2, 0) + t(1, 1, -1); (x, y, z) = (3, 4, -1) + s(2, 2, -2) c. x = 2 +t, y = 1 + 2t, z = 1 t ; x = -1 - 2s, y = -1 -1s, z = 1 + s d. (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. Find the point of intersection of the line (x, y, z) = (1, -2, 1) + t(4, -3, -2) and the plane x - 2y + 3z = -8. 4 Determine how the following lines and planes interact. a. (x, y, z) = (-1, 2, 3) + t(1, 2, 2); 2x + 3y - 4z + 9 = 0. b. x 2-t, y 3-t, z=-1+t; 3x y + 2z -1 = 0. 1. Determine how the following lines interact. a. (x, y, z) = (-2, 1, 3) + t(1, -1, 5); (x, y, z) = (-3, 0, 2) + s(-1, 2, -3) b. (x, y, z) = (1, 2, 0) + t(1, 1, -1); (x, y, z) = (3, 4, -1) + s(2, 2, -2) c. x = 2 +t, y = 1 + 2t, z = 1 t ; x = -1 - 2s, y = -1 -1s, z = 1 + s d. (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. Find the point of intersection of the line (x, y, z) = (1, -2, 1) + t(4, -3, -2) and the plane x - 2y + 3z = -8. 4 Determine how the following lines and planes interact. a. (x, y, z) = (-1, 2, 3) + t(1, 2, 2); 2x + 3y - 4z + 9 = 0. b. x 2-t, y 3-t, z=-1+t; 3x y + 2z -1 = 0.