Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (0, 0, 16), (12, 12, 0) (a) parametric equations (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) symmetric equations 12x = 12y = 16z − 4 x/12=y/12=(z-4)/16

Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 3x₁ + 3x₂ +6x3 = 12 - 9x1 - 9x2 - 18x3 = - - 36 - 6x2 - 18x3 = 18 Describe the solution set, x = O of the first system of equations in parametric vector form. Select the correct X2 X3 choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.) O A. X= B. X=X₂ C, X= D. X=X₂ + X3 3x₁ + 3x₂ + 6x3 = 0 - 9x1 - 9x2 - 18x3 = 0 - 6x2 - 18x3 = 0 + X3

Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x₁ +4x2 + 8x3 = 16 - 12x₁-12x₂-24x3 = - 48 - 6x₂ + 12x3 = 12 X₁ Describe the solution set, x= x₂ 4 X3 4x₁ + 4x2 + 8x3 = 0 - 12x₁-12x₂ - 24x3 = 0 - 6x₂ + 12x3 = 0 of the first system of equations in parametric vector form. Select the correct choice below and fill in the answer box(es) within your choice. (Type an integer or fraction for each matrix element.)