Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at the point (1, 3,2).

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

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Q: The surface z=f(x,y) intersects the plane x-2 along the curve C which has equation of dy Find at the…

A: Given Data: The equation of the curve is: z=13y3-y2 The point at which derivative is required is: x,…

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

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Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.5.…

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

Q: Find a point on the ellipsoid x + 3y² + z = 8 where the tangent plane is perpendicular to the line…

A: Introduction: The perpendicular vector to a 3D object f ( x, y, z ) can be calculated by computing…

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

A: Consider the equation of a plane as, ax-x0+by-y0+cz-z0=0 Here, a, b, c, are the slopes in x, y, z,…

Q: Find equation of line normal to plane 3x + 2y- z = 5 and pass through Drigin point.

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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 a vector equation of the normal line (the line orthogonal to the surface) for the surface…

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

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

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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).

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

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Q: Compute the equation of the plane tangent to the surface x^2+3 y^2+z^3 = 8 at the point (2,1,1).

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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: Find the area of surface x2 – 2y – 2z = 0 that  lies above the triangle bounded by the lines x = 2,…

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

A: Given:- x2+9xyz+y2 =11z2  To find:- Equation of normal line to the given surface at point (1,1,1)

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 the points on the surface ry + yz + zr - r - z = 0 where the tangent (5) plane is parallel to…

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Q: What is the equation for the tangent plane to the surface z = 4x°y2 + 2y - 2 at the point P(1, -2,…

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Q: Find the equation of tangent plane and normal lines of the surface: f(x, y, z) = 5x² + 4 y2 +z³-9 at…

A: Here we have to find the equation of the tangent plane and normal lines of the surface:…

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 the area of the surface obtained by rotating the curve x = 3 (y + 2)3/2, 1 <y< 2, about the…

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

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Q: A point moves along the intersection of the elliptic paraboloid z = 10x? + 3y² and the plane y = 1.…

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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: Consider the equation of the surface S given by: exyz + x3z3 − 3y4 = 9 An equation for the plane…

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Q: Find the equation oftangent plane and normal lines of the surface: ƒ(x, y, z) = 10x² –14 y² +11z³-7…

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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 surface 4 =1 at the point 16 9 (1,-3,2) O a.…

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Q: Find an equation of the plane tangent to the surface xy z2 = 2 at the point (2, 1, -1). %3D

A: Given that XY3 Z2 =2 And point (2, 1,-1).

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

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Q: Determine the equation of a plane parallel to x-z plane which is tangent to the circle…

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

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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: Let S be the surface given by the equation x^3+y^3-xz=5. What is the equation of the tangent plane…

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Q: area of the surface obtained by rotating the curve y=x^3, x ∈ [0

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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: b) Find the equations of Tangent plane and Normal line of the surface: z3 + xyz – 2=0 at Po(1,1,1)

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Q: Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use  inertia  to  classify  the  quadratic surface  given by equation. x2 + y2 + 2z2 −…

Q: A line intersects the xy plane at an x– intercept of N and a y intercept of F. Determine the volum…

A: Given:- A line intersects the xy plane at an x intercept of N and a y intercept of F.  To find :-…

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

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