Find the unit normal vector to the surface f(x,y) = y² – 4xy at (1,2). (a) i (b)- i (c) 8 i+4j (d)0 O a

Q: Find the work done by the force F = zi + xj+ yk in moving a particle along the curve x = t y = t²…

A:

Q: Find an equation of the plane tangent to the surface xy z = 2 at the point (2, 1, -1). O A.x + 6y +…

A:

Q: Q3 (a) Calculate the divergence of curl of vector F = e2=+y î + sin yz? j+ cos yzx k, V. (V x F).

A:

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(2, - 1, – 5) for the funct 2x…

A: Given that  fx,y,z=ln2xy-z

Q: Let f : R+ × R → R be the function f(x,y) = 2x + VTy³. (a) Find a tangent vector to the graph of…

A: The given function is: fx,y=2x+xy3 The given point is: 1,1,3

Q: A surface z = f(x, y) is defined implicitly by the equation x +y+ z – e² = 3 – e. - Determine the…

A:

Q: Let F(x, y, z) = xye" – 2° Ja and P(1,0, –1). Let S be the surface defined by the equation xye" –…

A:

Q: Sketch the level curve corresponding to c = 0 for the function given by           f(x, y) = y − sin…

A: We have given the function; f(x, y) = y − sin x This can be written as; z=y − sin x

Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Consider the ellipsoid 3x? + y? + z² = 11. The equation of the tangent plane to this ellipsoid at…

A: 3 x2 + y2+z2=11 and the point is (1,-2,-2)

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: (b) Verify your answer in (a) using Stokes' theorem, where the normal vector to the surface has a…

A: We have to apply Stoke's theorem.

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A:

Q: The directional derivative of a function f(x, y, z) = xy² – xz + y² at the point Po (1, –1,0) in the…

A:

Q: Compute (VxF). dS, where S is given by x² + y² + (z − 1)² = 2 and z ≥ 0, F(x, y, z) = (-esinzy, x +…

A: The general form of a vector-valued function is given by F1,F2,F3 where F1,F2 and F3 are the scalar…

Q: Find an equation of the tangent plane to the surface represented by the vector-valued function at…

A:

Q: Find a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A:

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: Let C be the curve of intersection of the paraboloid x? + y² = z and the cylinder + (y – 1)² = 1. 4…

A: We will find equation of common curve and parametrize it to find vector equation of C and the use…

Q: Find the equations of (i) the tangent plane and (ii) the normal line to the surface z = excos(y) at…

A:

Q: Find the directional derivative of the scalar function of (x, y, z) = xyz in the direction of the…

A: Given surface is z=xy

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: ii) Evaluate the vector line integral of F, F. ds, where y is an oriented curve defined as follows:…

A:

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

A:

Q: Q3 Evaluate Curlv•n , where i = 2xyi + (x – 2y)j+xzk and i is a unit vector normal to the surface…

A:

Q: Evaluate Curlv.ñ , where v = 2xyi +(x² – 2y)j + xzk and ñ is a unit vector normal to the surface…

A:

Q: 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…

A:

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: 2. Let z = f(x,y) = x³ + xe* +y?. (a) Find an equation of the tangent plane to the surface z = f(r,…

A:

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: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the fur 5x…

A:

Q: Consider the function f(x, y) = x³+2xy+y. (a) Give the linearization L(x, y) of f at (2,3). (b) Use…

A:

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

A: To find: The normal vector of the tangent plane to the surface at the given point. Given…

Q: Let P be the point (2, -1, 2) and Ø,: x² + y² – z² = 10. (i) Find the unit normal vector to the…

A: (c) The given surface is ∅1: x2+y2-z2=10 and the point P: 2,-1,2. (i) The unit normal vector to the…

Q: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A:

Q: Find the surface normal vector to the surface z 4-(x +y²) at the point (1, 1,v2) by (a) Vf (b) N =…

A:

Q: e the electric flux through a paraboloid z = x² + y² – 16 that lies . It is oriented by an outward…

A:

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 a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A: Here we use the concept of gradient of a scalar function at given point.

Q: Find a unit normal vector to the surface f(x, y, z) = 0 at the point P(4, – 5, – 5) for the function…

A:

Q: A force F acts on a particle that is moving in the plane along the semi-circle parameterized by 7(t)…

A: Work done W=∫CF.ds=∫abF(r(t)) . r'(t)dt   Where curve C is given by parametric equation r(t)

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…

A:

Q: E For the surface f(x,y, z) = tan(xy + %3D at (0,1,0) in the direction of ü = i- 2j +2k; (3) the…

A: Note- Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Find a unit normal vector to the surface f(x,

A:

Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

Q: Find the coordinates of the centroid of the curvex = cos t, y = t + sin t, 0 ≤ t ≤ p.

A:

Q: Suppose that over a certain region of space the electrical potential V is given by V (x, y, z) = 6x²…

A: We have to find the rate of change of V at point P in direction of v .

Q: nd a unit normal vector to the surface at the given point. [Hint: Normalize the gradient vector…

A: