3. Evaluate ox?y dx + xy? dy using Green's y 2 Theorem, where C is positively oriented by line y =x x = 0, y = x, and circle defined by x²+y² = 4. C 2.

Q: 2. Find the distance between the line with parametric equations ï = 1 + 2t, y = −2+ 4t, z = 4 − 4t…

A:

Q: .2 Use Green's Theorem to evaluate x-ydx - xy² dy , where C is the circle x +y² = 9 with…

A:

Q: A circle with center at the origin and radius equal to a meets the axis of x at A and B. P(a) and…

A: The coordinates of A are (-a,0) and that of P are (a cos α,a sin α)  Therefore,the equation of AP…

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

Q: b) Use Greens theorem to findf x² ydx – xy?dy where C is the circle x? + y? = 4 going counter clock…

A:

Q: Use Green's Theorem to find SF ·dř where F = (y³, –x³) and C is the circle x² + y² = 3. %3D %3D

A: The given vector is  F = y3i - x3j

Q: 10. Find the center and radius of the circle whose equation is x² + 5x + y² – 6y + 12 = 0. A.…

A: To find The center and radius of the circle.

Q: Determine whether the lines intersect, and if so, find the point of intersection. (If an answer does…

A: Explanation of the answer is as follows

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

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

Q: Evaluate (x + y)ds where C is the straight-line segment x = 4t, y = (12-4t), z = 0 from (0,12,0) to…

A: Let  where C is straight line segment  from .We know thatwhere

Q: 5. Evaluate - xy+3z)ds where C is the line starting at (1,1,1) and ending at (-1,-2,-3).

A:

Q: Sketch a contour map and graph of . a. g(x, y) = 9x² + 4y² b. z = y/x

A: The given function is: g(x, y) = 9x2 + 4y2 The contour map of the above function is:

Q: O COsZ Sc (5 dz T. 4 2

A: Consider the equation, z-π2=1 This equation represents a circle plotted on the Argand Plane, with…

Q: 3. Explain what is wrong with the following statement: If R,T are corresponding regions in the xy…

A:

Q: Let the circles C, :x + y = 9 and C2 : (x – 3) + (y – 4) = 16, intersect at the points X and Y.…

A: Sketch as per the conditions given:

Q: 4. Find the values of x and y as shown below if three lines are parallel. (5y-4) 3y (2x+13)

A:

Q: 2 Green's theorem, evaluate ((+) dx + 3xy dy where C is the circle * +y = 4.

A:

Q: Compute . Z+1 dz, where C1 is a part of a circle with r = 3, and 0<0< %3D

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Q: 1. Which of the following points in the standard (x, y) coordinate plane is farthest from the…

A: Which of the following  points in the standard (x, y) coordinate plane is furthest from the origin

Q: Find the equation of the line bisecting the acute angles formed between the lines x + 7y – 6 = 0 and…

A: The general equation of a straight line is y=mx+c, where m is the gradient, and y=c is the value…

Q: A. Determine the center and radius of the following circles. 1. (x - 4)2 + y + 8)? = 100 2. (x + 1)²…

A: I have answered first three subparts as per the guidelines.