Q1) Find equations of the Normal plane and Osculating plane of the curve y = 2t, x = 2 sin 3t , z = -2cos 3t at the point (0, T,-2).

Q: Find the parametric equations of normal line to the surface given by f(x,y) = tan Vx2 + y² at the…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(6,0,6) on the…

A: Use tangent plane equation

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: 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 the 'slope' of the tangent line to the curve of intersection of this surface 3z = 36-9x –4y?…

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Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, z = cos 3t at the…

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Q: Find an equation of the plane tangent to the graph of g(r, y) = 3ev²-z² at the point where (x, y) =…

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

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Q: find parametric equations for the line tangent tothe curve of intersection of the surfaces at the…

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Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — 3ху —у? -2…

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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…

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: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: Find the equation for the tangent plane and the normal line at the point Po(1,1,3) on the surface…

A: Given problem:- Find the equation for the tangent plane and the normal line at the point Po(1,1,3)…

Q: 8) Find equations of (a) the tan gent plane and (b) the normal line to the given surface at the…

A: Tangent plane: It is defined as the plane which passes through the surface of the points or it can…

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 parametric equations of the normal line to x² the surface z = + y? 4 at the point (2, -3, 10)

A: Given curve

Q: Find parametric equations of the normal line to the surface z = + y? at the point (2, -2,5) x = 2 -…

A: Let F(x,y,z) define a surface that is differentiable at (x0,y0,z0) then the normal line to F(x,y,z)…

Q: Find parametric equations for the line tangent to the curves of intersection of the surfaces xyz =1…

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Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x = 74…

A: given curves x2+z2=74 , y2+z2=74 , point 5,-5,7  to find parametric equations for the tangent line…

Q: 3. Find the unit tangent vector and principal unit normal vector for curve with parametric equation…

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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: Find the equation for the tangent plane and the normal line at the point Po(3,3,1) on the surface x…

A: To find an equation for the tangent plane and the normal line at the point (3,3,1).

Q: Find the equations of the tangent lines to the curve whose parametric equations are x = 2t2 – 4t +…

A: We find out dy/dx .then we find out value of t at given points and then find slope of tangent line…

Q: 12. Find an equation for the tangent plane to the surface given by 2xy = 2z2 - ryz at the point…

A: Use tangent plane formula

Q: b) Find equations for the tangent plane and normal line at the point P-(2, –3,18) on the surface…

A: x2+y-2xy-x+3y-z=-7   Let fx,y,z=x2+y-2xy-x+3y-z+7 and the point is 2,-3,18 Now,…

Q: The curve with parametric equationsx = (1 + 2 sin θ) cos θ, y = (1 + 2 sin θ) sin θis called a…

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Q: Find the equation for the tangent plane and the normal line at the point Po(3,2,3) on the surface 2x…

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Q: Find the equation of the osculating plane of the helix x = sin 2t, y = t, z = cos 2t at the point…

A: The helix is given as x=sin 2t, y=t, z=cos 2t. We have to find the equation of the osculating plane…

Q: 13. Find an equation for the tangent plane and the normal line to the surface x? + 2y? - 3z? = 3, at…

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Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y z 1…

A: Given:

Q: What is the moment of inertia of this area about the line y = -10 ?

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Q: Find the parametric equations of normal line to the surface given by f(x, y) = tan v x2 +y2 at the…

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Q: Find the slope of then tangent line to the parametric curve t t2 + 25, y 6. at t = -1 and t = 1…

A: Shown below

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: Find an equation of the tangent plane to the surface at the given point. x² + y2 + z2 = 33, (1, 4,…

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Q: 3. Find the equation of the plane tangent to xyz + x² – 2y² +z' =14 at (5,–2,3)

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Q: Find equations of the normal plane and osculating plane of the curve at the given point. x = sin 2t,…

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

A: We know that the equation of the tangent plane is: nxx-x0+nyy-y0+nzz-z0=0 Given:…

Q: Find the tangent plane and normal line equations to x+y +z =1 at the point (1, %3D -2, -4).

A: This question is related to 3D geometry and equations of plane and lines,  we will solve it using…

Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

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

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Q: Find parametric equations of the normal line to x2 the surface z = 4 + y? at the point (2, 3, 10)

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Q: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

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

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Q: 2) Find the cartesian eauation for the olar curve r=tan e sece ×ニy )yニxと 2.

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