Q5) Let f(x, y) = Find unit vector for which Duf(2,3) = 0. %3D x+y

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

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

A:

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: Find the directional derivative of f(x, y, z) = zy + xª at the point (2, 1, 3) in the direction of a…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

Q: Let F(x,y,z)=3x2+3y2+4z2. For which unit vector 0 will the directional derivative D0F at  (12,12,12)…

A:

Q: Find a unit vector n that is normal to the surface 2z^2−x^4−y^4=1 at P=(1,2,3) that points in the…

A: We have

Q: find a vector parametrization for the line with thegiven description. Passes through P = (4, 0, 8),…

A: The parametric equation of a line in vector for is given by the expression r→=u→+tv→. Here u→ is the…

Q: The vector n = (2, -3, 6) is normal to the tangent plane to z = h(x, y)at (1, -3, 5). Estimate…

A:

Q: Let F(x, y, z) =2x2+3y2+4z2. For which unit vector 0 will the directional derivative DoF at…

A:

Q: find the anit tang ent , norma and binor mal vector: el cost i a Sint tk]

A:

Q: Save : Among unit vectors (x, y), find one which maximizes r – 10xy + y. Record your answer correct…

A:

Q: (b) part of parabola y = −2x² from (−1, −2) to (2, —–8)

A: Given Equation of parabola y=-2x2 from -1, -2 to 2, -8.

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: f f(x, y, z) = xy: on of vectorî - %3D

A:

Q: Find a vector orthogonal to the line x+y=1

A:

Q: Two plane curves are defined by the vector functions r1 (t) = (t, 2t – 4) and r2 (u) = (2u, u²).…

A: r1t=t,2t-4 and r2u=2u,u2 For the intersection point, t=2u   ...1u=t22t-4=u2    ...2 Convert the…

Q: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7) r(t)…

A: Given: Represent the line segment from P to Q by a vector-valued function. P(7, 0, 9), Q(6, −6, 7)…

Q: Find the directional derivative of f(x,y,z)=yz+x^4 at the point (1,2,3) in the direction of a vector…

A: According to the given information, it is required to find the directional derivative.

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

A: Given: fx,y,z=3x+7yz 1,7,-1 To find: Maximum rate of change of f at the given point. The…

Q: Find a vector function that represents the curve of intersection of the cylinder x^2 +y^2 =1 and the…

A:

Q: why you write: s=0, t=0 s=1, t=1  instead of using cross product imediately between 2 vectors…

A: The vectors (1, 0, 1) and (1, -1, 0) are direction or orientation vectors. The cross product of…

Q: What is the magnitude of the vector v with initial point P = (-4, 3) and terminat piont Q = (2, -5)…

A: A detailed solution is given below

Q: Find unit vector tangent and normals to the are y=1/2 X3+1/2. Point(1,1)

A:

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

A:

Q: Given the function of two variables ƒ(x, y) = 4x³ − 60x² + 12xy² − 24y² +3. - - Find and classify…

A:

Q: Find the directional derivative of f(x,y, z) = yz +x? at the point (3, 2,1) in the direction of a…

A:

Q: Let f(x, y) = xe*²-v' and P = (1, 1). Find the rate of change of f in the direction of a vector…

A: The given problem is to find the rate of change of given function f in the direction of a vector…

Q: The directional derivative of f(x, y, z) = xyz at point (-1, 1, 3) in the direction of vector î - 2ĵ…

A: Remark: We know that the directional gives the rate of change of a function at a specific point in…

Q: Compute the lux of water through the OSIS3 if the velocity vector is v meters'sec. ( Generally. F-…

A: Introduction: Evaluation of flux of a vector field over a surface is an application of surface…

Q: Find a nonzero vector normal to the plane z − 5(x − 1) = −2(3 — y). - -

A:

Q: 2. For what values of h the vectors , ü2 = 9 ,ūz linearly independent? are

A: To find : For what value of h  given vectors are linearly independent    We have given the…

Q: . Let 7 - " be the separation vector from a fixed point (a', y', z') to the point (x, y, z). Show…

A: we have,  fixed point x',y',z'=r' and point x,y,z =r  r→-r→'=x-x'i^+y-y'j^+z-z'k^ a…

Q: If f (x, y, z) = xy + xz + yz, find this function's directional derivative at (-1,3,5) in the…

A:

Q: Q1) Find equation of plane normal to vector 3i + 2j – k and pass through point (1,1,5).

A:

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

A:

Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

Q: 7. If r = (x, y, z) and F vector r) is there a value p so that div F = 0? HE (where r| denotes the…

A:

Q: F(x,y,z)=2x2+7y2+7z2 F(x,y,z)= 1152 The unit vector u for which the directional derivative is…

A:

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

A:

Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

Q: Find a vector function that parameterizes the curve of intersection between the surfaces y^2-z^2=x-2…

A: To determine the vector function for the curve of intersection between the surfaces.

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Given information: The points are P(0, 0, 0), Q(5, 2, 2). Calculation: Find the vector valued…

Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.