Find the value of So(4x + y)dy- xydy where C is the path around the triangle in the counterclockwise direction with vertices (0,0), (2,0), (2,2). Assume the starting point is (0,0) State the value as a fraction in lowest terms:

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A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

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Q: Q8) The distance between the line x=-1+t, y3D3+2t, z=-t and the plane 2x-2y-2z=3 is: *

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Q: (x² +2y) where D is the triangular region with vertices (0, 1), (1,2) and (4,1).

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A: It will be solution of given Laplace equation only when, it will satisfy it.

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A: Use line integral

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A:

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Q: find the line of intersection of th e given planes. 3x + 2y + z = -1 and 2x - y + 4z = 5

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Q: Find the image of the line y = 5x + 7 under collineation a if a((x, y)) = (2у — х, х — 2)

A: Given that: Line is: y=5x+7and collineation is: (x, y)=(2y-x, x-2)

Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

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Q: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

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Q: Find the point at which the line y(t) z(t) = 2 + 4t -6-8t intersects the yz plane. 6-7t

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A: According to our guidelines we can only answer one question at time, rest you can repost. The given…

Q: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

A: Here I am attaching image so that you understand each and every step.

Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

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Q: xy dx + (x2 + x) dy, where C is the path in the figure below with vertices (-5, 0), (0, 5), (5, 0)

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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