1. a) Determine the symmetric equations for the line through P(5, 6, 10) and parallel to the line with equation , = (6, 1, 1) + 1(-2, 1, 3). b) Determine two other points on this line 2+3 2. Find the value of k so that the lines X - 3 _ y+6 X+7 y+8 2+9 and 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 7. Explain why there are many different vector and parametric equations for a line