Let F(x, y, z)=-y²i+xj+2²k, and let the curve C' be the intersection of the paraboloid z = ² + y² with the plane z = 20 - 2x - 4y, oriented counter-clockwise when viewed from above. Evaluate F. dr by

Q: Find the​ distance, d, between the point S(6,9,10) and the plane 10x+7y+1z=60.

A: Answer is 73/5√6.

Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find the point at which the line (-3, 3, 0) + t(-2, –3, –2) intersects the plane -2x – y + 3z = 5.

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Q: Let F(x, y, z) = -3y² + 4z + 6æk and C is the curve of the intersection of the plane x + y + z = 2…

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

A: Solution :-

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