Further Mathematics for Construction (CON4306) Assignment 1 Please submit your assignment on or before: 15 JUNE 2022 Hong Kong Institute of Vocational Education (Tsing Yi) Department of Construction Further Mathematics for Construction (CON4306) Assignment 1 1. Given A = 21 + 3) + 4k and B = 1 - 2] + 3k, find (a) A . B; (b) the acute angle between A and B; (c) the scalar component of A in the direction of B; and (d) A x B. 2. Two forces, F1 = 1 - 2j + k and F2 = 31 + 2j + 2k act through the point A(1, 1, 7) and B(3, 2, 6) respectively. Find (i) the moment of each force about the point C(5, 1, 4); and (ii) the resultant moment of the two forces about the point C. 3. A machine outputs a force F1 = 51 + 2j - 3k to move a box from the location with coordinates (1, 2, 3) to a new location with coordinates (7, 4, 8). Find the work done by the force output from the machine. 4. Given the following system of linear equation: 5x + 6y + 7z = 18 10x + 12y + 3z = 25 (20x + 17y + 19z = 56 (a) Solve the system using only Cramer's rule. (b) Solve the system using only Inverse Matrix Method. (c) Solve the system using only Gaussian Elimination. - End of assignment 1 - Page 1 of 1