9. Let W be the pyramid with top vertex (0, 0, 1), and base vertices at (0, 0, 0), (1,0,0), (0, 1,0), and (1,1,0). Let S be the closed boundary surface of W, oriented outward from W. Let F(x, y, z) = (x²y, 3y²z, 922r). Use Gauss' theorem to compute F. ds. F

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Given, through the point (4, 2, -5) and perpendicular to the plane…

Q: c) The surface S is the portion of the plane x+y+z=1 in the first quadrant of the Oxyz Cartesian…

A: Given: The surface and curve is shown below   The region s is the triangle and the curve C is the…

Q: 6. Find the intersection of the line / and the plane . 1:7=(4,-1,4) +t(5,-2,3) x: 2x+5y+z+2=0

A: Given is the equation of line as l:r→=(4,-1,4)+t(5,-2,3) Equation of plane as π: 2x+5y+z+2=0 First…

Q: Find the equation of the plane that contains the line x = 1+t, y = 2+2t, z = 3- (1, -2,4). e point p…

A:

Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: Q10) Find the equation of the plane passing through the point P(1,-1,2) and parallel to the line x-1…

A:

Q: 12. Find the vector with length 5 and direction angles a = B = 120°, y = 135°. = 60°,

A: 12. Given that a vector with length 5 and direction angles α=60o, β=120o, γ=1350.

Q: Exercise 1.19. Let P = (-1,1,7), Q = (1,3,5) and N = (–1,1,-1). Determine the distance between the…

A: Given Information: and .To find:The distance between the point  and the plane .Concept used: is just…

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: 3. Determine the intersection (if any) of the following planes. Show your work clearly ₁: 2x + 3y z…

A:

Q: For the convex set C = {(z,9)+ 13 y.0 < 2.0 < y } (a) Which points are vertices of C? (52/9,35/9)…

A:

Q: Determine the values of y such that D(9,3,-2), E(3,4,7) and F(21,y,-20) are collinear

A:

Q: Find the points on the sphere x² + y° + z?=1. that are closest to and farthest from the point (2, 1,…

A: Given, x2+y2+z2=1   ;   point (2,1,2)

Q: 20. Find the volume of the parallelepiped with adjacent edges u = (-2, 0.75, 4), v = (6, -0.3, 8),…

A: Solution :

Q: 2. Find the volume of the parallelepiped the following 3 vectors describe the edges: i.q=i-2j-3k, b=…

A: The given problem is to find the volume of the parallelepiped from the given following 3 vectors…

Q: 2. Consider the line r(t) = (4t+1,3, 2 - t) and the ellipsoid + + z? = 1. What is the distance from…

A: Consider the line  and the ellipsoid To find  distance from the point (-3,3,3) on the line to the…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Let L, be the line through the points (1,2,6) and (2,4,8). And let L2 be the line of intersection of…

A:

Q: 19. Find the distance from the point (3, -2,7) to the plane 4x – 6y + z = 5. Show all necessary work…

A: A detailed solution is given below.

Q: The plane z = Ax+By+C is to be "fitted" to the following points (XkYk Zk): (1,0,0). (1,0, -1),…

A: Let  S = ∑k=14 Axk+Byk+C-zk2  For minimizing S , we have  ∂S∂A = 0 ,  ∂S∂B = 0  and  ∂S∂C = 0…