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+32=-4 2x+4y+6z=10 b. 2x-y+2z=-8 4x-2y+4z=-16 c. x+3y-5z=-12 2x+3y-4z=-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+3x=- 2x+4y+6x=7 x+3y+2x=-3 b. x+2y+32-4 2x+4y+6z=7 3x+6y+9z=5 c. x+2y+z=-2 2x+4y+22=4 3x+6y+3x=-6 d. x-2y-2x=6 2x-5y 32 -10 3x-4y+z=-1 e.x-y+32=4 x+y+2x=2 3x+y+7z=9