If F= (xà) - ( x6), show that where r is the position vector and a,6 are constant vectovs

Q: Find a unit vector that is parallel to the line tangent to the parabola y = x2 at the point (6, 36).

A: The parabola y = x2 and the point (6, 36)

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: 3. Find the directional derivative Duf(x, y) if ƒ (x, y) = x³ – 3xy + 4y? and u is the unit vector…

A: First I have written the definition of directional derivative in the direction of given unit vector…

Q: Find the directional derivative of f(x,y)=yln(x+y) at the point (-3,5) in the direction of the…

A:

Q: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: This is a problem related to vector calculation. Based on the general formula we will find the…

Q: What is special about the derivatives of vector functions of con-stant length? Give an example.

A: What is special about the derivatives of vector functions of constant length

Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: Evaluate the directional derivative Duf (3, 4) if ƒ (x,y) = /æ² + y² and u is the unit V vector in…

A:

Q: An object moves with velocity vector (t,t?,-t) starting at (1,2,3) when t=0. Find the function r…

A: Since you have asked multiple questions so as per guidelines we will solve the first question for…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: Find the directional derivative of f(x, y, z) (2,1,3) in the direction of a vector making an angle…

A: Given the function f(x,y,z)=zx+y4

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

A:

Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

A:

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

A:

Q: Find the directional derivative of f(x,y) = x² + y² – 2x – 4y at the point (-2,3) in the direction…

A:

Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

A:

Q: Find the derivative of f at the point P( – 3, – 2) in the direction of = ( – 1, – 1) | -(– 3, – 2) =…

A: Given, f(x,y)=-0.02x2y3   (b) The directional derivative for a function f(x,y) in the direction of…

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: b. Find the directional derivative of the function z = x3 – y3 at the point M(1,1), in the direction…

A:

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

A:

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: Ex:- Find the directional derivative of fOxy,2) =X-xy-7 atRC,1,0) in the direction of vector A=21-33…

A: Solution is given below:

Q: e vector x²y?

A:

Q: Write down the vector equations of the tangent lines to the traces for /(r, 3) = re-y² at (2,0) for…

A: To write the vector equation of the tangent line for the below function to the trace y=0.…

Q: Find the directional derivative of f(x, y) = 10 − 3x^2 + (y^4)/4 at P(2, −3) in the direction of the…

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Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: Suppose z is given implicitly by the equation x3y-yz2+z/x=4 in a neighborhood of the point P (1,…

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: If (a,B), a<o is the unit vector that is parallel to the tangent line to the curve y=3x2-x at the…

A:

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: We need to find directional derivative.

Q: (#2) Evaluate the directional derivative Duf (3, 4) if f (x,y) = Vx² + y² and u is the unit vector…

A: The expression for the directional derivative of the function f in the direction of u at a point…

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

A:

Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

A:

Q: What is special about the derivatives of vector functions of constant length? Give an example.

A:

Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

A:

Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,gk = 0.

A:

Q: Compute the directional derivative of the function f(x,y) = - xy + y at the point P(0, - 9) in the…

A: Solution-

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

A:

Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: When is a vector incomprehensible and when is a vector irrational?

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Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

A:

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 self-value and self-vectors.

A:

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

A: Solution

Q: Find the derivative of the vector function ta x (b tc), where r(t) = (-1,1,-2) а %3 (-2,3, -1), ь 3…

A: Given vector function is,

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.