Evaluate the line mtegral over the curve S(-x + y +z) dx + (x+y - z) dy + (x-y +z) dz where the line vegnment prom (-1, 2,3) to (3,-2,1)

Q: Caleulate fe xydx + 3y'dy where C is the curve in xy plane, x = y from (0,0). to (1,3).

A: Solve the integral by substituting the curve in the question.

Q: Find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2)

A: We will find the minimum distance from the point to the plane x-y+z=3 at (1,-3,2) in the following…

Q: Q1) Find equation of line normal to plane 3x + 2y - z = 5 and pass through Origin point. 30 mark

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Q: Compute F. dr for the oriented curve specified. Jc F(x, y) = (6, y), quarter circle x2 + y? = 1 with…

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

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Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

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Q: Sketch the recion enclosed by the given curves. Decide whether to integrate with respect to rwr.Daw…

A: Draw all the regions first then decide which region satisfy all the curves

Q: 2) Evaluate the vategral if cis any Seetion al Smooth Curve from 10,0,0) to (lilil). .(-3p²+2y-Z) da…

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Q: bounded by the curve f(x)= Vx-1, y-axis, line y =1 and line y =

A: We will find the area bounded by the curves.

Q: Find the points on the surface ( y + z)^2 + (z - x)^2 = 16 where the normal line is parallel to the…

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Q: Find a vector which is tangent to the curve of intersection of the surfaces z = x² – y? and xyz + 30…

A: We will find out the required tangent vector.

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

A: We know that the parametric equation of a tangent line to the curve of intersection of the two…

Q: Find the length of the curve y =/2 from z = 0 to z = 3. %3D

A: Integration of (1+(f'(x))2)1/2 form 0 to.3

Q: Find parametric equations for the normal line to the surface z= 3x2 + 10y2 at the point (2, 1, 22).…

A: Given the equation of surface z=3x2+10y2

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: Determine equation of tnagent line to the common curve of 2 surfaces w/ equations: z = x? + y – 2xy…

A: follow next step

Q: Find equations of the Normal plane and Osculating plane of the curve x = 2 sin 3t , y = 2t, z =…

A: Given that x=2 sin3t , y=2t and z=-2cos3t and point 0,π,-2 find equations of the normal and…

Q: 2. Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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Q: Find parametric equations for the normal line to the surface x² + 9xyz + y² = 11z² at the point (1,…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, 3)…

A: First find the parametric equation of line passing through the points (0, 0) and (-1, 3).

Q: Determine the local linear approx imation of flx,4,z) =(1+x) (l-y³) (l-2)²' at the point CT, 2,3)

A: The local linear approximation: Lx, y, z of the function f(x, y, z) at the point x0, y0, z0 is…

Q: Write parametric equations for the tangent line to the curve of intersection of the surfaces x +y +z…

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Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

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Q: Find the slope of the tangent line at (-1, 1,5) to the curve of intersection of the surface z = x²…

A: According to question, we have, z = x2 + 4y2        .......(1)

Q: Determine the equation of the normal line to the surface z2 cos(x + 2y) at the point (2, –1, 0).

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Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find a set of symmetric equations for the normal line to the surface xyz = 12 at the point (2, −2,…

A: The normal line to the surface xyz = 12 at the point (2, −2, −3).

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Evaluate the line integral Sc (2x² − 3y) dx + xy dy, where the curve/path C is the line 3 y = 2/2 x…

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Q: Find an equation of the tangent plane to the surface x² + 2y² + z² = 175 at the point (5, -5, 10). O…

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Q: 5. Are there any points on the graph of x2 - y? – 22 = 1 where the tangent plane is parallel to the…

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Q: Compute ∫C(2x+√y)ds, where Cis the curve from (0,0) to (2,4) along y=x^2.

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Q: dz -, n = 2,3, 4, ... where z = a is inside the simple closed curve C. (z – a)" Evaluate

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Q: Find equation of line normal to plane 3x + 2y – z = 5 and pass througl Origin point.

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Q: Find equations of the normal plane and tangent line to the curve of intersection of the surfaces…

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

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Q: Integrate f(x,y,z) = x-3y + z over the line segment joining the points (0,0,0) and (2,2,2). %3D

A: Here, we need to integrate f(x, y, z)=x-3y2+z over the line segment joining the points (0, 0, 0) to…

Q: (a) Calculate the line integral (4x+2y²)dy where C' is the curve y = 2³, starting from z = 0, y = 0,…

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Q: Evaluate aned on c indicatid curve 2. 2. y+ Y( sm3x +ca 32,22 3t ,4=t,0zt2|

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Q: 4) Find the families of lines of curvature of the surface :=r+y

A: The answer is given in handwritten format --

Q: Calculate the curve integral ∫c ( 3x2 - 3yz + 2xz )dx + ( 3y2 - 3xz +z2 )dy + ( 3z2 - 3xy + x2 +2yz…

A: Using green's theorem to find the line integral.

Q: Compute F• dr for the oriented curve specified. F(x, y) = (9, y), quarter circle x² + y² = 1 with xs…

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Q: Let C be the curve on the xy-plane that is the projection of a horizontal cross-section of the…

A: Given that,

Q: Compute F. dr for the oriented curve specified. F(x, y, z) = (z³, yz, x), quarter of the circle of…

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Q: Let C be the curve which is the union of two line segments, the first going from (0, 0) to (-1, -2)…

A: Given: The curve C is the union of two-line segments, first going from (0,0) to (-1,-2) and the…

Q: Find the distance between the plane x+y +z = 3 and the line L= λ(1,0,-1).

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Q: Find all equations of normal line at the point (1, 1, –1) to the surface 2 +z² +3 = 2y + y?…

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Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).

A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…

Q: Determine the equation of the normal line to the surface z2 = cos(x + 2y) at the point (2, –1,0).

A: We have  z2 = cos(x+2y) ⇒cos(x+2y) - z2 = 0  So, F(x,y,z) = cos(x+2y) - z2  Thus,  ∇F(x,y,z) =…