a Complete the following and submit your work to the mpbox. Clu estion s 1. Determine the parametric and symmetric equations of the line through P(3= 1. -8} which is parallel to the line with equation F: (-2. 1. 3) + t[2.-3.1]. 2. Find the value of k so that the lines 3x + ky + z - 6 = l] and 6x + [1-k)y + 22 - 9 = l] are perpendicular. 3. Determine parametric equations for the plane through the points Nil1.4]. 8(3. 1. 8). and CH. 1. 3}. 4. Determine a vector equation for the plane that is parallel to the zaxis containing the line r = (1. 2: -1} + tl{3, 1, 2). 5. Determine a scalar equation ofthe plane through the point {4. l] -1] and parallel to the plane r= {2. -1 4] + 9(2. 0. 3) +t[-3. 2. -5}. 5. Determine a vector equation of the plane that contains the origin and the point [2. -3. 2} and is perpendicular to the plane x + 2}; z + 3 =0. II". Find the intersection. ifany. ofthe line (L522) = (2. 1. 4} + t (1.111) andthe plane 3x 4v 32 9 = l}. 8. Solve the following system of equations and give a geometrical interpretation of the result. x+y+z=1 x + 2y + 3: = 3 x + 4y + 62 = 5 9. Give a geometrical interpretation of the intersection ofthe planes with equations x+y+z+3=0 2x+3y521 = U 4x+5y-122+ 11 =0 10. Determine a scalar equation for the plane that passes through the point (1= 1. 4] and is perpendicular to the line of intersection of the planes x+2y+z=1and2x+y+32=3 11. A line has the equation r = 5110.0] and a plane has the equation y=1_ a] Describe the line. b] Describe the plane