t-) For each surface below, find the normal vector and equation of the tangent plane at the given point. (a) z = (x² + y²)%; (2,2, 2) (c) z = y tan(x)' (T/4, 1, 7/4). (b) z = esin(ry); (T/2,1, e) (d) z = x"; (3,4,81)

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: Q1: Find the tangent plane and normal line of the surface F(x,y,z)=x² + n + y² + z² = 10 at point…

A: Given :            F(x, y, z) = x2 + 2x + y2 + z2 - 10             Point P0(1, 1, 1)

Q: Find parametric equations of the normal line to the surface z = 4 +y? at the point (2, 3, 10) O x =…

A: To Find:  the parametric equations of the normal line to the surface  z = x24+y2 at the point ( 2,…

Q: Find equations for the tangent plane and the normal line at point Po (Xo.Yo.Zo) (5,2,0) on the…

A: The equation of the surface is -cosπx+2x2y+4exz+4yz=105. The function is fx, y,…

Q: Find the slope of the tangent line at the point (1,−2,−3) on the curve of intersection of the…

A: Given surface is z=5-4x2-y2 The slope of tangent line to the curve that is the intersection of the…

Q: Find a vector tangent to the curve of intersection of the surfaces given by x² + y² + z² = 1 and 2²…

A:

Q: Find the tangent plane and normal line to the surface f (r, y) = In (2r + y) at the point (-1,3,0).…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the angle of inclination of the tangent plane to the ellipsoid                           x2/ 12…

A:

Q: Find parametric equations for the tangent line at (1, 3, 3) to the curve of intersection of the…

A: First, find the function of the surface in three variables, f(x,y,z).  f(x,y,z)=x2y-z Find the…

Q: Find the equation of the tangent plane to the surface y = 2x2 - z2 at the point (0, –1, –1) %3D | |

A:

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

A:

Q: Find an equation of the tangent plane to the surface z=8/2x+4y at the point (2,1,1). z=

A: Please see the explanation below

Q: Find the equation for the tangent plane to the surface x- 5xyz+ y = - 7z at the point (- 1, -1, -…

A:

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

A:

Q: 8. Determine the equation of the plane tangent to z point (x, у, z) 3 (-2, 1, 4). x*y3 at the =

A:

Q: Find the points on the surface 6x² + y² – 3z² = 4 where the tangent plane to the surface is parallel…

A: We need to find points of intersection.

Q: Find equations for the tangent plane and the normal line at point Po (X0,Yo,Zo)(1,5,0) on the…

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

Q: Find the normal vector to the surface z = xe™Y at the point (2,0, 2).

A:

Q: The equation z = f(x,y) = y +x -3y defines a surface. What is t- equation of the tangent plane at…

A:

Q: /Find the equation for the tangent plane and normal line to the surface Z = 9-x² + y² at the point…

A: Given eq. of surface z=9-x2+y2 at the point 1,2,4             (1)

Q: Find an equation of the plane tangent to the surface sin(xyz) = at the point (T, 1,-)

A: sinxyz=12 at the point π, 1, 16. Consider, sinxyz=12⇒xyz=sin-112⇒xyz=π6⇒z=π6xy Differentiating…

Q: Solve for an equation of tangent plane and parametric and symmetric equations of normal line to the…

A: Given Surface is xz + 2xy + yz = 10

Q: Find the equation on the plane tangent to the following surfaces at a given point: z=exy; (2,0,1)…

A: The equation on the plane tangent to the surface z = f(x, y) at a given point (a, b, c) is given by:…

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

A:

Q: Find equations for the a) tangent line and b) normal plane to the curve made by the intersection of…

A: Given The given surfaces are 3x2y+y2z=-2 and 2xz-x2y=3.  The given point is 1,-1,1.

Q: Find an equation of the tangent plane to the surface z = In(x - 2y) at the point (3, 1,0) %3D

A: Given that, z = ln (x - 2y) we have to find the equation of tangant at point (3, 1, 0).

Q: Find an equation of the tangent plane to the surface zx + 2xy + 3yz3 = 6 at a point in the…

A:

Q: Find the equation of tangent plane and normal lines of the surface: ( x, y, z) = 5x^2 +  4y^2 + z^3…

A: We have to find the equation of tangent plane and normal lines of the surface: f(x,y,z)=5x2+…

Q: Find an equation of the tangent plane and a parametric description of the normal line to the surface…

A:

Q: Find the plane tangent to the surface z = x cos y - yex at (0, 0, 0).

A: Consider the following function: z=fx,y=xcosy-yex Differentiate function fx,y with respect to x:…

Q: Find the point (x, y, z) on the surface z = 2x2 - y where the tangent plane is parallel to the plane…

A: We have to find the point (x, y, z) on the surface z = 2x^2 - y^2 where the tangent plane is…

Q: A normal vector to the tangent plane for the surface a y"z* = 1 at the point (1, 1, –1) is: %3D…

A:

Q: The equation of the tangent plane to the surface defined by z y exp(-x) at the point (0, 1, 1) is =…

A: equation of the tangent plane

Q: The two surfaces x2 + y2 + z2 = 6 and 2x² + 3y2 + z2 = 9 intersect at the point(1,1,2). Find the…

A: Given: The two surfaces  x 2 + y 2 + z 2 = 6  and  2 x 2 + 3 y 2 +  z 2 = 9. The given two surfaces…

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

A:

Q: Find the moments of inertia about the coordinate axes of a thin rectangular plate of constant…

A:

Q: (a) Find equation of the tangent plane and normal line to the sphere x + y +z = 25 at the point…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

A:

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

A:

Q: find an equation for the plane tangent to thesurface z = ƒ(x, y) at the given point. z = 1/ (x2 +…

A: Concept - Equation of plane is given by - Ax-x0+By-y0+Cz-z0 = 0         ...............(1)where,x0,…

Q: Find an equation of the tangent plane and symmetric equations of the normal line to the surface zx2…

A: Given the equation of the surface can be rearranged in the form F(x,y,z)=0 zx2-xy2-yz2-18=0 Here,…

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

A: Given vector rt=2sin3t,2t,-2cos3t. Then r't=6cos3t,2,6sin3t. The given point is 0,π,-2. Now the…

Q: Find the equation of the tangent plane and the normal line to the surface x +y = 6xyz +8z2 at the…

A:

Q: Q2: Determine the tangent plane and normal line to the surface x^2+2xy-y^2+z^3=7 at point (1,-1,3)

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 2. Find an equation of the tangent plane to the parametric surface F(u, v) = (, 2uv, uv?) at the…

A: (2) Consider the provided question,

Q: Find the equation of tangent plane to the surface x? + 2y? + 3z2 = 21 which is parallel to the plane…

A: equation of the tangent surface of  F= x2+ 2y2+ 3z2= 21   which is also parallel to the plane…

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) =…

Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

A: