d the normal vector to the surface y = 16x at (4,8). (a) 16(f-j) (b) (1 – f) (c) 6(1 – 1) (d) none of these

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface.3.…

A: To find equations for the(a) tangent plane and(b) normal line at the point P on the given surface.…

Q: At time t, a particle moving in the xy-plane is at position (x(t), y(t)), where x(t) and y(t) are…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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Q: Find parametric equations for the normal line to the surface z=-7x2 -9y2   at the point   (2,1,-37)

A:

Q: Exercise (2): Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to…

A: We have to find the line integral

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A: NOTE: Hi! Thank you for the question. As per the honor code, we'll answer any one question in case…

Q: 6. Find the unit vector for which the directional derivative Duf(x,y) of f(x,y) = %3D 3x2 + 4y2 at…

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Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2).

A: Please check step 2 for the solution.

Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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

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

A:

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…

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Q: Find parametric equations of the normal line to the surface z = 4 + y² at the point (2, –2, 5) |

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Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

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Q: Find a vector normal to the surface 3z 3 + x 2 y - y 2 x = 1 at P =(1,-1,1) .

A: Given: 3z3+x2y-y2x=1 at P(1,-1,1)

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).

A:

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

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Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 3, 11) for the function…

A: The unit vector normal to the surface f(x, y, z)=0 is ∇f∇f. where ∇f = fx, fy, fz and ∇f = fx2 + fy2…

Q: 2. Find a unit normal vector to the surface x + y +2 = 5 at the point (0, 1, 2). Ans. Û + 2k)

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+…

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Q: 4. Find the equation of the tangent plane to the surface ey + In(xz) – evz = 0 at the point (1,0,…

A: Given:

Q: Choose the normal vector of the tangent plane to the surface defined by Z = e6x²+14xy-5y² at the…

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A:

Q: 9. Find an equation for the tangent plane and the normal line to the surface xy + yz + zx = 5 at the…

A: f(x,y,z)=xy+yz+zx-5=0,  at  (1,2,1)now we differentiate above equation with respect to x,y,z…

Q: 8. Find the curvature of the vector-valued function r(t) = at the point t = -1.

A: given function is rt=3t2,-4t,1t find the curvature at t=-1 k=r→'t×r→''tr→'t3

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

A:

Q: 3. Find the equation of the tangent plane and the equations of the normal line to the surface z = In…

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Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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Q: Find a unit normal vector to the surface at the given point. x²y3 - y?z + 2xz3 = 4 (-1,1, –1)

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Q: Find parametric equations for the normal line to the surface -10x + 5y + 9z =3 at the point (1, -…

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Q: Choose the normal vector of the tangent plane to the surface defined by z =e4x²+16xy-9y2 at the…

A: Explanation of the answer is as follows

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: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

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Q: 2. Compute the vector line integral: -y х — 4 Le (x – 4)² + y² dx + (x – 4)2 + y² dy where C is the…

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Q: Find a vector function that represents the curve of intersection of the surface 4x+2y-8z^2=16 and…

A: To find a vector function that represents the curve of intersection of the surface 4x+2y-8z2=16 and…

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

A:

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: Which of the following give the symmetric equations of the normal line to the surface xy + yz + zx =…

A: Normal to the surface is a line perpendicular to that surface.

Q: find equations for the(a) tangent plane and(b) normal line at the point P0 on the given surface. x2…

A: GivenSurface F(x,y,z)=x2+y2+z2-3=0Point of…

Q: Find the equation of the tangent plane to the surface 4. =1 at the point 16 9. (1,-3,2) O a.…

A:

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) =…