Please answer the following questions in full:

1. a) Determine the symmetric equations for the line through P(5, 6, 10) and parallel to the line with equation F = (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 x - 3 _y+6 z+3 and X +7 y +8 2+9 3k +1 2 are perpendicular. 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 ) .7. Determine the intersection, if any, of the planes with equations x + y - z + 12 =0 and 2x + 4y - 3z + 8 = 0. 8. Solve the following system of equations and give a geometrical interpretation of the result. x+y+z=6 2x+ y - 3z =-5 4x - 5y + z = -310. Determine a scalar equation for the plane that passes through the point (2, 0, -1) and is perpendicular to the line of intersection of the planes 2x + y - z + 5 = 0 and x + y + 2z + 7 = 0