Let C be a circle lying in the plane x+ z = 2 with center at (1,0, 1). Evaluate the line integr V2 dy + -y 1 z dx + 2(z- 1)2 + y2 dz. 2(x – 1)2 + y?

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: Integrate counterclockwise dz, C the circle with z2 + 12z + 35 center –5 and radius 2. dz z2 + 12z +…

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Q: Find an equation of the tangent plane to the surface z = -2z² – 2y?- lz 2y+ 3 at the point (5, 1,…

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Q: Evaluate √(2² + yz sin(xyz))dx+(y²+xz sin(xyz))dy+(x+xysin(xyz))dz where C is the curve following…

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Q: Compute F. dr for the oriented curve specified. F(x, y) = (4x2, xy), line segment from (0, 0) to (2,…

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Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

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

A: Solution :-

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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