Set up the iterated integral for evaluating| f(r,0,z) dz r dr de over the given region D. D is the prism whose base is the triangle in the xy-plane bounded by the x-axis and the lines y =x and x = 4 and whose top lies in the plane z= 6- y.

Q: What is the distance of the origin to the plane through (√3, √3,0), (√3,0, √3) and (0,√3,√3).

A: We have to find the distance of the origin to the plane passing through  and .

Q: Find an equation of the line tangent to the intersection of the cylinders x² + z² = 4, y² + z² = 4…

A: The parametric form of the tangent line is  x=x0+aty=y0+btz=z0+ct where, (a,b,c) is the direction…

Q: x+1 y-3 Find the equation of the plane containing line =

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Q: 2) = ( (x, y, z) =

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Q: Find the equation of the plane through the line of intersection of the planes x+y+z=1 and…

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Q: Solve for the distance between the point P(0,0,0,0) and the plane w + x + y + z = 3 in R^4.

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Q: Find a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Find the point on the sphere x^2 +y^2 +z^2 =4 which is closer to the point (1,-1,1)

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Q: / Find the distance from the line x 2 + 1, y 1 +1, z = -(1/2) - (1/2)t to the plane x + 2y + 6z 10.

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Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Find the equation of the planes that contains two lines given by L₁ :x=1-2t, y = 4 + t, z = t and…

A: Given that the lines are             L1: x=1-2t, y=4+t, z=t, L2: x=2-3t, y=1+4t, x=2-t. To find 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: the midpoint of line segment with end points (-1,6,2) and (3, 2, -4) What is the distance between B…

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Q: definition set and drawan the plane Find the

A: Using elementary properties of logarithmic function and square root function set is obtained then…

Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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