1. Linear Algebra Question

Question #1 [5 marks] Consider the parallelogram with vertices P(1, 2}, 0(9, 4). R(8, 1), and 3(0, 3). + H a. Verify that the vectors PQ and PS are two adjacent sides of the parallelogram using the parallelogram rule for the addition of vectors (Le. by showing that i > PQ + PS results in PR). b. Use the formula for a 2 x 2 determinant to nd the area of the parallelogram. Question #2 [7 marks] + + Consider the points 11031, 2, *1), 3(71, 71,7), and 612,5, 5). where a1 6 R and direction vectors CA and 03 are perpendicular. > } a. Find CA - CB and use the result to find a]. ) ) b. Knowing that CA and CB are llnearly independent (they are perpendicular from part (8)). state a vector form of the equation of the plane that goes through all three poinE. ) > c. Determine CA x CB and use the result to find a standard form (i.e. scalar form) of the equation of the plane that gas through all three points in a simplied form