Let f, u and S be scalar, vector and (second-order) tensor fields respectively. Using index notation, or otherwise, prove the identity V· (fS"u) = f(V · S) · u + SVƒ · u + fS : Vu. Compute all quantities appearing in the above identity to verify its validity when f(x) = x1*2, u(x) = S(x) 0 0 = I2

Q: Calculate Vf using suffix notation and the chain rule: ƒ(r) = 3(a ⋅r)² − a²r² (a is a vector…

A:

Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Write the vector v = B - 3 8 {[][]}· 8 -2 as a coordinate vector with respect to the basis

A:

Q: Determine whether the vector functions, x1(t)= [ et ]           [ -et ] and x2(t)= [ et ]…

A:

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Find a vector G with curlG = sin xk.

A: Let F → = d1i+d2j+d3kThen curve F → =∇xF → =ijkddxddyddzf1f2f3Let us consider G→ = g1i+g2j+g3kThen…

Q: Find the angle between the surfaces x² + y² + z² = 49 and z = x² + y² - 7 at the point (3,-2, 6):

A: Since you posted multiple questions, as per Bartleby guidelines we are answering here first…

Q: Sketch the vector fields. Use a table for it.    F(x,y)=<x,y-x

A: Sketch the vector field Make a table to sketch the vector field. Table should have values (x,y)

Q: (d) s(v+ww) × (rv)

A: Given that u→,v→,w→∈ℝ3 and r ,s ∈ℝ.

Q: Find the directional derivative of the scalar field = xy + 4xz at the point (2, -2, 4) along the…

A:

Q: {} Find in R² whose coordinate vector relative to the basis B is [x]B Let B = x = 12 -5 -6 [:] 5

A: Introduction: The coordinate vector of an element of vector space related to basis is the vector…

Q: Determine the basis that generates the following vector space by clearing the variable y: M = {(x,…

A:

Q: Fill in the table and then sketch the vector field. z| y F(z, y) = (, %3D 20 0 2 -2 -2 2 -2 -2| -2 2…

A: Here, to fill the table and then plot the vector filed.

Q: Describe all solutions to Ax = 0 in parametric vector form for 1 -3 2 0 5 A - 00 00 1 2 0 -1 000 1 0…

A:

Q: Find a non-zero vector i perpendicular to the vector i

A: See the attachment

Q: Let V = {f: R→R: fis continuous}. V forms a vector space under the "usual" addition and scalar…

A:

Q: Expand the 3D pollutant transport equation in vector notation into individual differential equations…

A:

Q: Consider the vector-valued function. (a) Show that is continuous at t = -1. (b) Evaluate (R. RY(2).…

A: Like a scalar function, features like continuity and differentiability are also demonstrated by…

Q: If T is a mixed tensor, then T} + T{ is generally not a tensor a tensor May or may not

A: Answer : may or may not  Hence, Option (iii) is true.

Q: Describe all extensions of the identity map of ℚ to an isomorphism mapping ℚ(3rd root of 2) onto a…

A: