Answer:
The base is 8 and the height is 3, so the area is 8 (3) = 24 square units.
Step-by-step explanation:
The area of the parallelogram is given by the following expression:
[tex]A = \|\vec u\times \vec v\|[/tex]
The vectors are, respectively:
[tex]\vec u = (10-2, 1 - 1,0-0)[/tex]
[tex]\vec u = (8,0,0)[/tex]
The base of the parallelogram is 8 units.
[tex]\vec v = (8-2, 4-1,0-0)[/tex]
[tex]\vec v = (6,3,0)[/tex]
The height of the parallelogram is 3 units.
The cross product of both vectors is:
[tex]\vec u \times \vec v = (0,0,24)[/tex]
The area of the parallelogram is given by the norm of the resulting vector:
[tex]\|\vec u \times \vec v\| = 24[/tex]
