1. Use normal vectors to determine the interaction, if any, for each of the following pairs...

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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 a line, determine a vector equation of the line. a. x + 2y + 3z = -4 2x + 4y + 6z = 10 b. 2xy + 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. 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 a line, determine a vector equation of the line. a. x + 2y + 3z = -4 2x + 4y + 6z = 10 b. 2xy + 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.