I would prefer the answers typed out but if you MUST use paper be clear and neat. Answer each question correctly and briefly explain how you got the answer. Use your knowledge of Lines and Planes specifically for this! Thanks!

1. a) Determine the symmetric equations for the line through P(5, 6, 10) and parallel to the line with equation ; = (6, 1, 1) + t(-2, 1, 3). b) Determine two other points on this line 2. Find the value of k so that the lines 2-3 _ y+6 z+3 and x+/ y+8 z+9. are perpendicular. 3k +1 2 2k 3 -2k -3 3. Determine parametric equations for the plane through the points A(2, 1, 1), B(0, 1, 3), and C(1, 3, -2). 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through the point (4, 1, 3). 5. Determine a scalar equation for the plane through the points M(1, 2, 3) and N(3 ,2, -1) that is perpendicular to the plane with equation 3x + 2y + 6z + 1 =0. 6. Show that the line with parametric equations x = 6 + 8t, y = -5 + t, z =2 + 3t does not intersect the plane with equation 2x - y - 5z - 2 =0