3.use Greens theorem S(1+x dx + 2xy dy ,where C is triangle With vertices (0,0),(1,0).(1,3) oriented clockwise (3) Hinit (oく-1,3 (し) py (1 + x*)- dx + 2ytan-'xdy ,where C is closed curve xi + yi = 1 maa Al

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Lo and Li are lines in 3-space whose parametric equations are Loix = x0 + aot, y = yo + bot, z = zo…

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Q: Draw the contour curves for h (x, y) _y²+x² -1+2x and c = 0, 2, 4.

A: If the graph of z=f(x,y) is sliced by a plane: z=c, then the two dimensional cross-section obtained…

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

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Q: Consider the point (3,4,5) What is the projection of the point on the xy-plane?

A: The given point is (3,4,5).

Q: Point ZZ is located at (-5,-3)(−5,−3) on the coordinate plane. Point ZZ is reflected over the…

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Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: 18. What is the rectangular equation of the curve whose parametric equations are x = 2t, y= 2+ 3t*?…

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Q: Find the equation to the conicoid generated by lines parallel to the plane XOY, intersect OZ and the…

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Q: Show that the line of slope t through (-1, 0) intersects the unit circle in the point with…

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Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: 11) A point on the surface 2x + y? + z? = 4 at which the tangent plane is parallel to the plane x -…

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Q: Line A goes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A and passes…

A: Given: Line A passes through the points (4, −1, 0) and (1, 5, 2). Line B is parallel to line A. Line…

Q: Q5/A// Find the distance between the point P =(2, 1, 1) and line L:x = -2+ 5t, y= 2 +4t, z = -3-6t.…

A: Use distance formula

Q: calculate S S, y³ dA where Ris the vertex of the triangle (0, 2), ( 1,1) and (3, 2)|

A: In this question we have to calculate the following integral.

Q: It can be shown that the parametric equations x = x1 + (x2 – x1)t, y = y1 +(y2 – yı)t, where 0 <t 1,…

A: Given: Parametric equation of line segment joining the points P1x1,y1 and P2x2,y2 is given as…