Please show step by step workings and make it very neat and organized please. PLEASE DO HANDWRITTEN CLEAR WORK. For example- mathematical Step by Step workings:.... Thus Answer: ....

1. Given the vector equation for each plane, rewrite the equation in scalar form. a. P = (1, 0, 1) + s(2, - 1, 3) + 1(2, 1,-2) b. T = (2, 3, 4) + s(1, 1, 1) + t(3, 1,-1) C. T= (3, 2, 1) + s(1, 0, 1) + 1(2,-1, 3) d. T = (5, 1, 1) + s(3,2, 3) + t(0, 1,-2) 2. Given the scalar equation of a plane, rewrite the equation in vector form. a. n : x - 3y - 32 = 4 b. 12 : 1x - 72 = 1 C. n3 : 2x + 2y - 1z = 9 3. Determine the point of intersection between the line r = (1,-5,3) + ((3,2,-1) and the plane m : 2x + 3y - 7z = 11 4. Determine if the point P(1,2,1) lies on the plane n, : x - 3y - 3z = 4. 5. Given the points A(3,2,1), B(-4,1,7) and C(2,0,0). Determine the scalar equation for the plane they form. 6. Given the point P(1,2,1) determine the shortest distance to the plane m : xty+z = 1 7. For each set of planes determine the type of intersection and state the solution set for each. a. x + 2y - 3z = 8 b. x + 2y - z = 4 c. - 3x + 6y + 16z = 36 x + 3y - 5z = 11 2x + 5y + z = 10 x - 2y - 5z = - 11 2x + 5y- 8z = 19 4x + 9y - 1z = 19 2x - 3y - 8z = -17 8. Determine the following projections: a. proj (1,0,1) (2, 1, 1) b. proj(1,-2,1) (5, 1, 2) c. proj(0,1,-1)(4, 4, 2)