Find the surface area of the part of the plane z = 4 + 3x + 7y that lies above the rectangle [0, 6] x [0, 6].

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

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Q: prove that [(1/₂) = √T by using the definition of error function.

A: We have to prove that τ12=π by using the definition of error function.

Q: What does 2x + y = 4 represent in the xy plane and what in the space?

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Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: Find the trace of the plane 3x − 2y + 5z = 4 in the xy-plane.

A: The given equation of the plane is 3x-2y+5z=4. The trace of the plane in the xy-plane is the…

Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

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Q: Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

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Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: Determine a so that the line x-3/a=y+5/2=z+1/4 is parallel to the plane 2x+3y-5z=14.

A: To determine  so that the line  is parallel to the plane .

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…