(₁) Find the volume of the parallelpiped R³ whose corner points (0, 0, 0), (1, 1, 1), (2, 2,5), (1,3,3) and their sums.

17 A box has edges from (0, 0, 0) to (3, 1, 1) and (1, 3, 1) and (1, 1, 3). Find its volume. Also find the area of each parallelogram face using ||ux v||.

List the vertices in R² of the convex region defined by Ax ≤ b and x > 0 where A = 3 and b = 5 9 (A) (2,3), (2, 2), (2.0), (0,0), (0,4) (D) (3,2). (). (2,0), (0,0), (0, 3) (G) (3,2), (2, 2), (2.0), (0,0), (0, 3) (B) (3,2), (2, 2), (2.0), (0,0), (0,4) (C) (3,2), (2, 2), (2,0), (0,0), (0.4) (E) (2, 3). (.). (2.0), (0.0), (0,4) (F) (2,3), (2.). (2.0), (0,0), (0, 3) (H) (2,3), (2), (2.0), (0,0), (0, 3)

List the vertices in R² of the convex region defined by Ax ≤ b and x ≥ A = 1 2 and b = 2 5 (A) (2,3), (½, ²), (2,0), (0,0), (0,3) (D) (2,3), ( ½, ³), (2,0), (0,0), (0,4) (G) (3,2), (½, ²), (2,0), (0,0), (0,4) where (B) (3,2), (½, ½), (2,0), (0, 0), (0,3) (E) (2,3), (½, ½), (2,0), (0, 0), (0, 3) (H) (3,2), (½, ½), (2,0), (0, 0), (0, 4) (C) (2,3), (2, 2), (2,0), (0,0), (0, 4) (F) (3,2), (3, 1), (2,0), (0,0), (0, 3)