Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate planes. (Assume that C is oriented counterclockwise as viewed from above.) F. dr where F = (x + 6z)i + (8x + y)j + (10y −z) k_and C is the curve

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

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Q: Determine the Cartesian equation of a plane that has x-, y-, and z- intercepts 1/3, 1, and -1/2,…

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Q: Represent the line segment from P to Q by a vector-valued function. P(4, 0, 7), Q(3, -3, 4) r(t) =…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Determine an equation for the plane that's tangent to the surface z = 6x2 + 7y2 at point (-3, -2,…

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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: Let L. be the line passing through the point P-(4, -3, 1) with direction vector a-[-4, 1, 1], and…

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Q: Find the distance between the point (0,0, 8) and the plane given by 2x – y + 2z – 1 = 0.

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Q: Consider the plane x-y-z-8= 0. Find the point in this plane closest to the point (1, 0, 1).

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Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

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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: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain