00:01
In this problem, we are given the vector field, v is equal to negative 3i minus 2j minus 3k, we are asked to calculate the flux outward through a given rectangular region with a is equal to 1 and b is equal to 2.
00:28
Consider the given rectangular region.
00:31
So here using the value of a and b we can say the rectangular region passes through the point 002, 012, 112, 110 and 1000.
00:47
That is this rectangular region is the part of the plane that is passing through these points.
00:56
Now given these points we can evaluate the the equation of the plane passing through this points as 2x plus z is equal to 2.
01:12
And now the flux of this given vector field outward through this rectangular region is by formula integral over the region as f.
01:26
Dot da is double integral over the region are in the xy plane.
01:36
The vector field f dot product with negative fxi minus fyj plus k dx, where the surface s is in the form is that is equal to f of xy.
01:58
So here the surface s is the plane 2x plus z is equal to 2 which can be written as z is equal to 2 minus 2x which is of the form is said is equal to f of xy.
02:12
So that we have fx is negative 2 and fy is 0...