Let F = -9zi+ (xe"z – 2xe"* ) } + 12 k. Find f, F · dÃ, and let S be the portion of the plane 2x + 3z = 6 that lies in the first octant such that 0 < y < 4 (see figure to the right), oriented upward. Z| Find the flux of F through S. Show your work, and circle your final answer.

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: The midpoint between the points (6, -7, -2) and(-2, 1, 4) is

A: The solution of the problem is given in the next step.

Q: 2 A -3 -1 -1 -2 The midpoint of AB = ([ ? ], [ ])

A:

Q: 9 Find the distance from the point (-7,-3,4) to the xy-plane.

A: Distance of a point (a,b,c) from the plane lx+my+nz=p is (la+mb+nc-p)/sqrt(l^2+m^2+n^2)

Q: ,1), (2, 2), (1, 3), (4, 1), (3, 2), (2, 3), (1,4), (5, 1), .... Show that this constitutes a proof…

A: We will answer the first question only as we don't answer multiple questions at a time. Please…

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A:

Q: If (-2, 3), (4, -3) and (4, 5) are the mid-points of the sides of a triangle, find the coordinates…

A: On solving this we will get:-

Q: Describe the plane x = 4.

A: Given, plane x=4we have to describe the plane x=4

Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…

Q: Describe the graph of the equation. r= (7 - 21) i + 8rj O Itisa line in 2-space through the point…

A:

Q: Find the equation of the plane parallel to the line r = 2i + t(-4i + 8j + 8k) and containing the…

A: We have to solve the given problems:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.