Question

Find the vector representing the area of the rectangle with vertices and oriented so that it faces downward. The magnitude of the vector equals the magnitude of the area; the direction is perpendicular to the surface. Since there are two perpendicular directions, we pick one by giving an orientation for the surface

Answer 1

Answer:

The answer is  "-72 k".

Explanation:

Please find the complete question in the attached file.

Given point:

$A=(0,0,0)\\B=(0,8,0)\\C=(9,8,0)\\D=(9,0,0)$

$\bar{AB} = (0i+8j+0k)-(0i+0j+0k)= 8j\\\\\bar{AC} = (9i+8j+0k)-(0i+0j+0k)= 9i+8j$

Calculating the area:

$Area=\left|\begin{array}{ccc}i&j&k\\0&8&0\\9&8&0\end{array}\right|$

       $=i[8(0)-8(0)]-j[(0-0)]+k[(0-9(8))]\\\\=i[0-0]-j[(0)]+k[(0-72)]\\\\=i[0]-j[(0)]+k[(-72)]\\\\=-72 \ k$