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: Find parametric equations for the line through the point P(3, 6, 4) that is parallel to the plane x…

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Q: how was it determined that the equation of the yz plane is x = 0?

A: The objective is to explain yz-plane equals .

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

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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: 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: Li Syaoran is riding an airplane which departs from an airport located at (360, 0) miles in the…

A: The westward speed of the airplane = 480 miles/ hour The northward speed of the airplane = 120…

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: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

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

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

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: 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