4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are symmetric.

Q: Prove that if u is the vector function with the constant value C, then du/dt = 0.

A:

Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

A: Stretched distance = 42-30 =12  cm = 0.12 m  Let F=kx [ by Hooke's law ]  So,

Q: let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove that…

A:

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A:

Q: Let x be an n-vector. (a) Is it possible for x · x to be negative? Explain. (b) If x · x = 0, what…

A: We shall define, x→=(x1,x2,...,xn) The dot product of two vectors x→ and y→ is given as,…

Q: Suppose it takes a force of 30 N to hold a spring that has been stretched from its natural length of…

A: Given, F= 30 N x1= 6 cm= 0.06 m x2= 8 cm= 0.08 m

Q: If A is second order tensor , then |A| =T^i

A:

Q: The vector E %3D —а, — 4аф + За, еxpressed in RCS and in terms of ф is E 3 (-сosф + 4sinф)ax +…

A: This question is based on unit vector conversion from Cartesian to cylindrical system.

Q: Given a cubic force in one dimension: F = a(x – a) (x – b) (x – c), find the coefficient k in the…

A: Substitute x=b+∈ F=αx-ax-bx-c  =αb+∈-ab+∈-bb+∈-c  =α∈∈+b-a∈+b-c  =α∈∈2b-a+b -c∈b-ab-c…

Q: of the vector PP2• -ppositely direct to PP2 and whose norm is the doubl he same direction as PP.…

A: Consider the given point as, P11,-2,1 and P2-1,3,0

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

A:

Q: (b) Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that ·…

A:

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,9k = 0. %3D

A:

Q: Suppose that a particle following the path c(t) = (t,t – 5t,0) flies off on a tangent at to = 3.…

A: Given:c(t) = (t2 , t3-5t , 0)

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,-3) to (3,-9).

A: Given force is F→=xyi^+y-xj^ and straight line coordinates are 1,-3 and 3,-9

Q: The divergence of the vector F = a²yî + æyz} – a*y°k is x2 y? k is -

A:

Q: Q2/ Show that the vector v = ai + bj is perpendicular to the line ах + by + с.

A: A line and the vector  are said to be perpendicular to each other when the product of their sloped…

Q: is Cartesion Tensor o& orden 2 on the for m 3 a=(3,4,1) Find - 2 %3D Tią and a. I

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

A:

Q: prove that kronecker and Livi-civita are tensors of rank 2 and 3 and respectively?

A:

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

A:

Q: Suppose C is a curve of length N, and ||F|| < M, where M is some positive number. Prove that F. dr <…

A:

Q: Use the definition of the divergence to show that div(c, F, + c2F;) = c, div(F,) + cz div(F,) for…

A: F1, F2 : D ➡️ R3 are differentiable vector fields and for constant c1 and c2 we have to prove that…

Q: Given: kk ij + 2με Find the invariant form of strain tensor in terms of stress.

A: The complete solutions are given below

Q: In Fr let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A:

Q: Suppose that C has length 5. What is the value of F. dr if: (a) F(P) is normal to C at all points P…

A: Given: Length of C is 5. (a) F(P) is normal to C at all points P on C. ∫CF→·dr→=∫CFdrcos90°=0…

Q: 2) If A =,find grad(div A), where r is a position vector.

A:

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

A:

Q: Suppose it takes a force of 21 N to hold a spring that has been stretched from its natural length of…

A:

Q: Find the net outward flux of F =axr across any smooth closed surface in R, where a is a constant…

A:

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: Suppose r(t) is a vector function in R3 Show that if r(t) has a constant speed, then r′(t) is…

A:

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

A:

Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

A:

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

A:

Q: If A is second order tensor ,then ylgn O ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The dimension of the vector space P; is equal to: Select one: O 5 none of the others 4

A:

Q: The unit tangent vector of a(t) =cos 2t e, +stn 2t e, - tez at t = is

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: ind the norm of x and the unit vector u in the direction of a if -5 * = ||| = %3D 2 2

A: The norm of a vector A→=abc is defined by A→=a2+b2+c2.

Q: Q1/A/ Show that in plane the non zero vector N = ai+ bj is:- perpendicular to the line ax +by +c =0…

A: We have to show that the vector N=ai+bj is perpendicular to the line ax+by+c=0. We have to find the…

Q: 12. Suppose that ú = (a, b) is a non-zero vector in R², where a ± 0. Show that the line L =…

A:

Q: prove that 1 Ə div A; = {√g grk Ak} = div A¹, Əx* where A; and Ai are the covariant and…

A:

Q: Show that the vectors (1- i, i) and (2, –1 + i) in C“ are lincarly dependent over C but linear…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.