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 the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: w=f(z)=z/(1-z) under transformation IzI=3 Find the image of the circle?

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Q: Evaluate |2*(x +7) – 2y ds C where C is the circle of radius 1 centered at (-3,0) and lying on the…

A: Since the integral ins on the plane x=-3 so the integral becomes:  ∫Cz3x+7-2yds=∫Cz3-3+7-2yds…

Q: let l={(x,y) 7x+4y=1} be a line in Cartesian model for Euclidean geometry. find a coordinate…

A: Given: I=x, y 7x+4y=1 represents a line in Cartesian model.   To find: A coordinate function using…

Q: Show that the line x + 1 =y/−1=(z − 2)/2 is in the plane 2x + 4y + z = 0.

A: Given equation of a line, x+1=y-1=z-22 And equation of a plane, 2x+4y+z=0

Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

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: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: i y-jx x* + y* Q.5 (a) Compute |F.dr, where F and c is the circle x + y = 1 Use parametric equations…

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

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: Integrate counterclockwise dz, C the circle with z2 + 16z + 63 center –7 and radius 2. dz z² + 16z +…

A: Use Cauchy Residue theorem to evaluate this integral.

Q: Find the distance between the plances 3x +y-4z = 2 and 3x+ y- 4z = 24

A: Find the distance between the planes   3x+y-4z=2    and    3x+y-4z=24

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

A: Solution :-

Q: Evaluate |*(x + 7) – 2y ds where C is the circle of radius 1 centered at (-3,0) and lying on the…

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