u = (-7, 7), v = (1, –1) (a) Find u · v.

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

Q: The directional derivative of the functionf (x, y) = -y at the point (–3, –2) in the direction of…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. Rx, Y,…

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

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Q: Find the directional derivative of the function at the given point in the direction of the vector…

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Q: Find the directional derivative of f(x, y, z) = z3 – x²y at the point (5, -2, -2) in the direction…

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Q: x = X, +(-

A: let the initial velocity be v0 , and the initial distance be x0 .and in time t , the new velocity…

Q: p) What is the directional derivative of /(x,y,z)=(x+2y+3z)* at point (1,-1,1) in the direction of…

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

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Q: Find the rate of change of the functionf(x, y) = x^2 + 3xy at the point(3, 2) in the direction of…

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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: 2. Find the gradient vector at the indicated point f(x, у, 2) 3 ху — In (2),. (2, -2,2)

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Q: 5. Find the directional derivative of f(x, y) = y² + (x²/y), at the point (2, 1) in the direction of…

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Q: The directional derivative of f(x, y) = -xe²y – x³y at the point (0, 4) in the direction of the…

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Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: 1 u (-y°i +x rmal vector to

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Q: Ex.: Find the directional derivative of the function f(x, y) x'y + x'y at the point (1,1) in the…

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

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Q: find the gradient of function f [x, y,z] = 3x² -y?_z? at paint {i,-Ź, -¡}

A: The given function is fx,y,z=3x2-y3-z2 and the given point is 1,-2,-1. The gradient of the function…

Q: The directional derivative of f(, y) = In(x² + y²) at the point P(1,5) in the direction v (3, 4) is…

A: We have to find the directional derivative of the function fx, y=lnx2+y2 at the point 1, 5 in the…

Q: determine wave direction in the function f(x,y) x^y — x²y³ decreases faster at the point (2,-3)

A: Wave direction in the function f(x,y)= x4y-x2y3 that decreases faster at the point (2,-3) is…

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

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Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x2 + y2 = = 81…

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Q: af Calculate at point (-1,2) where f (x, y) = 8+ x² + 3y? dv and v = i+j. 10 2 5/2 V2

A: fx, y=8+x2+3y2  &  v=i+j Partially differentiating with respect to x, we get fxx, y=0+2x+0=2x…

Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

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: #1. Find the directional derivative of the function f(x,y,z) = x²y + 2y2z at the point (1,–2,0) in…

A: Given:

Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: frxy, 2) =x*j+ x2 +xyZ direction of ū - (1,2,3) 10 5 in the

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

Q: Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Concept Used: Maximum rate of change of f(x, y, z) at point (p, q, r) occurs in the direction of…

Q: Let v = (3,4, 12) . Find the directional derivative of f(x,y, z) = x – y² +3z³ in the direction of…

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Q: ctor Calculus ints possible (ungraded) AS 2) Find the directional derivative of f(a, y, z) = x² + y…

A: Answer and explanation is given below...

Q: Find the directional derivative of the function f(x, y) = In(x +y°) at the point (2, 3) in the…

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

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: a. Find the direction in which the directional derivative of f(x,y), at the point (z, y) = (0,4),…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Given: Function f(x, y, z) = x2y + y2z , point (1, 5, 6) and vector v = <2, -1, 2> To Find:…

Q: 3 Find the directional derivatives of p = 8xyz³ - 2x²y²z² at the point (2,-1,1) in the direction 21…

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Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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Q: Eavluate the gradient vector at the given point. a) f(x,y) = cos2(πxy) at (1,-1) b) f(x,y,z) = xeyz…

A: a) Given function is

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: In differential geometry give me example of covariant tensor and contra variant tensor.

A: Concept:

Q: p1. Find the directional derivative of o = x²z+ 2xy² + yz? at (1, 2,-1) in the direction of vector…

A: on using gradient we get

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A:

Q: Find the directional derivative of f(x, y, z) = z - x²y at the point (-3, -2, 4) in the direction of…

A: According to the Bartleby guidelines only one question can be solved at one time, post the second…