Let D be a simple region in the plane R2 and P(x, y) and Q(x, y) be C¹ functions. Then Green' theorem states that др ду aD от ( of ( of / ( ) - Jap - ) = p + ) - J ду ду ƏD др дх ду aD от ( 9 ) - Jop o ( + ) - D до I до дх ду AD до дх др до дх ар ?x = Pdx + Qdy - Pdy + Qdx до = Pdx + Qdy = Pdx + Qdy = Pdx + Qdy

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: x+1 y-3 Find the equation of the plane containing line =

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Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: 2) = ( (x, y, z) =

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Q: Which of the following is the equation of the plane that is pas the point P(2, 2,–2) and vertical to…

A: Given, the equation of the plane that is passing through the point   P(2, 2,-2) and vertical to the…

Q: Which of the following is the equation of the plane that is passing through the point P(2, 2,–2) and…

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Q: Calculate the distance from point s(10, -8, 10) to the plane 2x + 2y + z = 4 O 10 O 10 의 ~m 의 29

A: Given query is to find the distance between the plane and point. The given point is S(10, -8, 10)…

Q: Prove that for all n E N, 1 1x 2 x 3 n(n + 3) 4(n + 1){n + 2 1 1 2 x 3 x 4 n(n + 1)(n+2)

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Q: G(x,y)= (x+3y) / (x^2 - y^2 ) Sketch the domain

A: G(x,y) = x + 3yx2 - y2 The denominator cannot be zero. Therefore, x2 - y2 ≠ 0(x+y)(x-y) ≠ 0x ≠ -yx ≠…

Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: If x and y are two n-vectors, then prove that 1 1 (a) x'y< I,l»,- +=1 (Holder incquality) P 9 (b)…

A: Answer :- A) Ans :-

Q: the normal line of the surface [z = (4x^2 + y^2] at the point (1,1,5) O 8x-2y+z=5 O 8x+2y+z=5…

A: We have to find the normal line of the surface.

Q: af of H.W: Find and for the functions: b əx ду 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2)…

A: Given functions are 1. f(x, y)=(xy-1)2 3. f(x, y)=(x2-1)(y+2) 4. f(x, y)=x(x2+y2)   To Find: ∂f∂x…

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: (5) Consider the plane defined by x+y+z+5= 0. Let (ro, Yo, zo) be an arbitrary point in R³ and let…

A: The equation of the plane is given by:.Let  be an arbitrary point in  and  be the point in the plane…

Q: The distance from (-2,-5,-6) to the yz-plane is (A) -2 (B) 2 (C) (D) -5 (E) 6

A: Use distance between two points

Q: 3 find +he equation of Hhe plane perpendicul av bo the plane x+24+5z=|| and passing through the…

A: The given plane is,

Q: Justify that (•, ·) defines an inner product on R?. the function (', ·) defined on R? as follows: U1…

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Q: Let C be the line segment joining M(-1,3,4) to O(0,0,0) and C' be the line segment joining O(0,0,0)…

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Q: 123. If F is a vector point function and a is a constant vector then show that i) V (a · F) = (a-V)…

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Q: Let C[0, 1] be the vector space of continuous functions that are defined on the interval [0, 1].…

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Q: Determine whether u, v and w lie in the same plane when positioned so that their initial points…

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Q: The plane given by x + y + 2z = 0 and the line given by x = 2 + t y = 1 - 2t z = 3 + t

A: The plane given by x + y + 2z = 0 and the line given by x = 2 + t;  y = 1 - 2t ;  z = 3 + t To find…

Q: Find the equation of the planes that contains two lines given by L₁ :x=1-2t, y = 4 + t, z = t and…

A: Given that the lines are             L1: x=1-2t, y=4+t, z=t, L2: x=2-3t, y=1+4t, x=2-t. To find the…

Q: Evaluate the following integral using a change of variables. R y-x y + 2x + 1 4 dA, where R is the…

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Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

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Q: Find √x²ds ds along the line of intersection of the two planes x-y+z=0 and x+y+2z=0, from origin to…

A: The two given planes are x-y+z=0 and x+y+2z=0.