Hello I need some help with these 3 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. Use normal vectors to determine the interaction, if any, for each of the following pairs of planes. Give a geometric interpretation in each case and the number of solutions for the corresponding system of linear equations. If the planes intersect in a line, determine a vector equation of the line. a. x + 2y + 3z = -4 2x + 4y + 6z = 10 b. 2x - y + 2z = -8 4x - 2y + 4z = -16 c. x + 3y - 5z = -12 2x + 3y - 42 =-6 2. a. Determine an equation of the line of intersection of the planes 4x - 3y - z = 1 and 2x + 4y + z = 5. b. Find the scalar equation for the plane through (4, 5, -3) and perpendicular to that line of intersection. 3. Use normal vectors to determine the intersection, if any, for each of the following groups of three planes. Give a geometric interpretation in each case and the number of solutions for the corresponding linear system of equations. If the planes intersect in a line, determine a vector equation of the line. If the planes intersect in a point, determine the coordinates of the point. a. X + 2y + 3z = -4 2x + 4y + 6z = 7 x + 3y + 2z = -3 b. X + 2y + 3z = -4 2x + 4y + 6z = 7 3x + 6y + 9z = 5 c. X + 2y + z= -2 2x + 4y + 2z = 4 3x + 6y + 3z = -6 d. x -2y -2z = 6 2x - 5y + 3z = -10 3x - 4y + z=-1 e. X - y + 3z = 4 x + y+2z = 2 3x + y+7z = 9