Evaluate f. F.dr, where F(r, y, z) = z?i+rj and C is the boundary of the square {(r, y, z)|0 < x < 1,0

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Q: The plane 7= [1,0,0]+t[1,1,1]+s[L,−1,1]; s,t €R contains the point (3,0, p). Find the value of p.

A: Given r=(1,0,0)+t(1,1,1)+s(1,-1,1)

Q: Find a parametrization of the line in which the planes x- 2y - 2z = 3 and -3x + 3y + 3z = -6…

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Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: 2) Draw contour maps for functions f(x, y) = x² - 4y², and g(x, y) = x² + 4y². What shape. are these…

A: The contour of function f(x,y) represents parabolas.

Q: 6 (A) 2x-yS6 (B) 2+y<6 (C) 2-y26 (D) +2y26

A: The solution are next step

Q: Use Stoke's Theorem to evaluate $. F · dR, where F (x, y, z) = (z²,xy, xz) and C is the triangle in…

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Q: If (x, y) and (X, Y) are the coordinates of the same point referred to two sets of rectangular axes…

A: and are the co-ordinates of the same point referred to the set of rectangular axes with same origin.

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y +z = 1 that lies above the…

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Q: hat is the scalar equation of the xy plane?

A: Given query is to find the scalar equation of the XY plane.

Q: Evaluate v (x? v + x y z²) · dr where C is the line segment from (1, – 1,0) to (2,1,3) | Select one:…

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Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: a) Mark the points on the contours where Iz = 0. b 2.

A: A contour line or level curve is the intersection of a surface with a horizontal plane. For example…

Q: 8) Given z =f (x.y) =1- (x² +4y2) ,Find : a)The vector function, 10 normal to the surface of f at…

A: This is problem of vector calculus.

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: Ex: Find egns of the line thru the pt ( -!,), perpendicular bo the line 3x= 2y == and paralled to…

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

A: Solution :-

Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: The slope of the surface z = xy² in the x- direction at the point (2, 3) is O 12 O 8 O 1 O 9 O 10

A: The slope of the surface z = f(x,y) in the x-direction at (x0,y0) is given by [∂z/∂x](x0,y0) =…

Q: Consider the curve F(t) that represents the intersection of the surfaces x + y? -1=0 and y= 2x a.…

A: Given: The curve r(t) represents the intersection of the surfaces x2+y2-1=0 and y=z/2x.

Q: a) Evaluate ff, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the…

A: Surface integral

Q: ScF· dĩ, where F(x,y) = (6x - 2y)7+x²7, and C is the line segment Evaluate from (6, -3) to (0, 0).

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Q: Find the coordinates of the point (x, y, z) on the plane z = 4 x + 1 y + 2 which is closest to the…

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Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…