Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2), (0, 2). Use Green's Theorem to evaluate the line integral 3y²x dx + 3x²y dy.

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

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Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

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Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

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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: 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: 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: Please

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Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: 24 Resolveu = [8, 3, 5] into rectangular components, one of which is collinear with v = [3, 1, 2].

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Q: point P(1, 1, –3) and orthogonal to the plane 3y – 4x + 2z = 3. |

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Q: Find the point - on the sphere (x - 4)² + y² + (z − 8)² = 1 nearest to the point (6, 0, 8).

A: To find the point on the sphere((x−4)2+y2+(z−8)2=1)that is nearest to the point ((6, 0, 8)), we'll…