Verify Stoke's Theorem. F=< y, –xz,xz² >, C'is the boundary of the paraboloid z = x² + y² lying pelow z = 1 plane. Assume C is oriented CCW.

Q: Let the surface S: x + y? +z? - 14x – 7y + 14 = 0. Which of the following is true? 3/39 O A.S is a…

A: Given The surface equation is S: x2+y2+z2-14x-7y+14=0 .

Q: b. Find the projection of v with equation 2x -y + 4z = 0. 1 -3 on the plane

A:

Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: Let H be the segment of the hyperbola x-y°= | Connecting (1,0) to (2, J3). Evaluate the line,…

A: Given  H be the segment of hyperbola x2-y2=1 connecting the points (1,0) to (2,3)  we have to…

Q: H.W: Find the distance from S (1,1,3) to the plane 3x+ 2y+ 6z = 6

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Q: . Consider the plane P : x +y + z = 2 and point A(0,1, 2). A line L has the parametric equations L:…

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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: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

A: Consider the given parabola y2=4ax Suppose Ax1 , y1  and  Bx2 , y2 be the ends of the focal chord of…

Q: 2. Evaluate ([.(Vx F). ds, where S is the surface of the paraboloid x2 + y2 + z = 4 above the…

A: We have given F→=(x2+y-4)i+3xyj+(2xz+z2)ksurface is given x2+y2+z=4 and above the xy planediagram of…

Q: es v3x + z – 5 = 0 and 2x + 2/3z + 10 = 0. ond

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Q: Closest point is (If there is more than one point, enter a comma-separated list.)

A: