Considering the scalar functions = ¢ (x, y, z) and Y = Y (x, y, z), fınd the value of the following expression? V.* (V 0 × V¯ Y) =?

Q: Find a function f(x, y, z) such that Vf is the constant vector (4, 8, 2). (Use symbolic notation and…

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Q: Considering the scalar functions P = 0 (x, y, z) and Y = 4 (x, y, z), find the value of the…

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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: considering the scalar function (x, y, z) = 9x³y - 2x√√z z calculate a)what is the gradient ofo b)…

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Q: I. Given the scalar function f (x, y, z) = exyz and vector function F(x, y, z) = -z i + xj - y k.…

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Q: Cives とz f(xy)= J36-9メ-す i) Find domajn and Ram ge Foy the fuclien

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Q: VECTOR DIFFERENTIATION:   If d(^2)A/dt^2 = 6t i - 24t(^2)j = 4sintk, find A given that A = 2i + j…

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Q: Find a function f(x, y, z) such that Vf is the constant vector (3,2, 8). (Use symbolic notation and…

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Q: (x" + 2x + 4y = 0 ly" + x + 2y = 0 x(0) = y(0) = 0 %3D x' (0) = y'(0) = -1 of bee %3D ondeplo no…

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Q: ) Jar t, < t 3 tz+ operator DP(x), stating cle scalar equation ÿ + y3 VI

A: The one to one function is shown as,

Q: Halle F· dr, -yi +xj y x² + y2 donde F (x, y) = C* es la semicircunferencia x² + y? = 1 (y 2 0)…

A: We find the given line  integral using parametrization.

Q: Find a function f(x, y, z) such that Vf is the constant vector (4, 5, 3). (Use symbolic notation and…

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Q: Find a parametrization of the tangent line to r(t) = (In(t))i + t-°j+ 3tk at the point t = 1. (Use…

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Q: 1. True or False: It's possible for the directional derivatives of a given function along two…

A: Solution-1)

Q: 5. Let the temperature T in a body be independent of z so that it is given by a scalar function T=…

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Q: 2. Find the directional drevative of f(x, y,z) xsinyz at the point (1,3,0) in the direction of v = i…

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Q: a) Rewrite the expression P= f(Q, D, 52, P,H) in dimensionless form by using Pi- theorem, where P is…

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Q: Find the domain of the vector-valued function given below. r - (1) = V9 – 12i + + (sin 1) k→…

A: To find the correct option

Q: 21 Work Find the work done by the force F = xyi + (y – x)j over the straight line from (1, 1) to (2,…

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Q: An object is moving along the x-axis from x = 1 (Point a) to x = %3D 2 (Point b) according to the…

A: As per guidelines we are solving one question .Please re-post other question.   Given:…

Q: Find real differentiable functions s(y) and t(y), such that the complex function f(x + iy) = e"…

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Q: f(z) = Cosz %3D ,0< Izl f(2) = sinz 3D 0< zl %3D f(z) = e-V, 0< Izl %3D

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Deternime the equation of the tangent plane to the surface givne by the equation G(u, v) = (u^2 –…

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Q: A scalar function F(x,y,z) = xy2 + x2z – z2y. Find the gradF at (1,1,1).

A: A scalar function is given. We have to find the gradient at a specified point.

Q: Find a function f(x, y, z) such that Vf is the constant vector (7,5, 4). (Use symbolic notation and…

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Q: Integral of Vector A= 2p sin(@)ap +0.5z2cos(9)az along L1 4Y L2 L1 180° L3 30° -5 0. 12.5 20 -12.5

A: integral of vector a = line integral (A.dl) from given figure  we will A.dl then we will calculate…

Q: Pr. #1) Find the directional derivative of h at the given point in the direction of the vector v.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a function f(x, y, z) such that Vƒ is the constant vector (9,5, 2). (Use symbolic notation and…

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Q: Transform pentagon BEARS according to (xy) → (x + 6, y+8). Write the coordinates for pentagon…

A: Given Data: Traformation: x, y→x+6, y+8   The given figure in the problem represents the pentagon…

Q: Q5:- a-Solve the initial value problem for r as a vector function of t. d'r (sin t)i- (cost)j + (4…

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Q: I. Given the scalar function f(x, y, z) = e*yz and vector function F(x, y, z) = -2 i + x j- yk. Find…

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Q: Find the integration of the function f(u) = u(u+ 4) +u-4 + /[u +5) + J((u + 4)) %3D

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Q: A force F(x) = 10−2x N applied in the positive x-direction moves an object 3m from x = 2to x = 5.…

A: Given that , Fx=10-2x N Work (W)=?

Q: (4)Find the scalar function such that F = V ø y i+ where F=- *+y x+y

A: We can find scalar function ϕ such that F→=∇ϕ ;where ∇ =i^∂∂x+j^∂∂y+k^∂∂z

Q: 5. Express the flowing quantities in rectangular form. a) sec( + j1) cot(17/12 + j3 cosh(2 + j3) b)…

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Q: 3.An object moves along the parabola rít) = (t, t), 0 sts1.subject to the force F (1/(y + 1), -1/(z…

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Q: V = [3x-y, x² -ky²] In the force field defined by the vector, a particle moves from point A(-2,-1)…

A: We have to find the value of k

Q: Given vector valued function Q(t) = a. Reparametrize using arc length from point A(2,1,3) to…

A: Given Vector Valued function             Qt=t3+2, -2t3+1, -2t3+3In part(a) we have to reparameterize…

Q: rove that Vx(F)= 0 tor any scalar function

A: Cross product of the scalar function

Q: Q3A) Using Cauchy Riemann equations show that: f(z) = 2z8z5 + 4z6 4z38z² + 2z is analytic in…

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Q: I. Given the scalar function f (x, y, z) = exyz and vector function F(x, y, z) = -z i + x j – y k.…

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Q: A particle moves along the graph of y = cos r so that the r-component of acceleration is always 2.…

A: Use the given information carefully.

Q: Find a function f(x, y, z) such that Vƒ is the constant vector (9,7,7). (Use symbolic notation and…

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Q: (1) Give an example of a function z = f(x, y) and a unit vector i such that f(0,0) = 2, fy(0,0) = 1…

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Q: Find curl(7z i + 8x j+ 5y k). curl (7z i + &x j+ 5y k) = ( i )i + (i )j + ( )k

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Q: 2. A block of mass 68 kg rests on a horizontal floor. The coefficient of friction between the block…

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Q: Exercise I f(1, y)yz (a) Let f(r,y) = rỷ - . Then deduce that f(1,y)zy (Clairaut's theorem). %3D

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Q: for the function given:  a) Show that the function has any vector derivative in the direction of the…

A: Definition: Directional Derivative Directional derivative of f(x, y) at a point p(a, b) in the…

Q: Örnek : |z – 2| = 1 C eğrisi üzerinde I = f. cos z dz z(z²-2) - integralini hesaplayın.

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Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.