Consider the vector field F(r, y, z) = (2ry³z*, 3x²y²zª, 4x²y³z³). (i) Show that F is a conservative vector field and find o such that F = Vø. (ii) Use this to evaluate F. dr, where C consists of the line segment from (1,0, -2) to (1, 1,0) followed by the curve given given by r(t) = (e', cos (t), t) for 0

Q: Compute the curl of the following vector field. F= (3x-y,5xy,2) The curl of F is (Di+ (Di+(Ok.

A: F=3x2-y2,5xy,2zCurl F(x,y,z)=∇XF→(x,y,z) where ∇=∂∂xi+∂∂xj+∂∂xkCurl F(x,y,z)=ijk∂∂x∂∂y∂∂zFxFyFz

Q: Which of the following functions V can be considered a vector field. Select all that apply. V: R² V:…

A: Multiple numbers of functions are given in the given data.Find out the vector field?

Q: Represent the following equation functions. (a) (r – h)² + (y – k)² = r²

A: We have given an equation (x-h)2+(y-k)2=r2. Represent given equation as vector valued function.

Q: If F is a vector field then V. F is a vector field Select one: True False

A: If F is a vector field then ∇·F is a vector field

Q: Write formulas for the vector field with the given properties. (Assume the vector field is two…

A:

Q: For a given vector field calculate (V.) – (V · Ñ ) + Ý × ( ▼ × V) O||XV|| OV2 O-V2

A: We need to find a simplified calculation of the given vector field expression.

Q: (d) div( 3xi +2yj) = (e) div( -5xi – 5yj) =

A: We have to find the divergence.

Q: (a) For all vectors ū, v, w e R³, w x (i x ũ) = (w x i) ×ũ. True False (b) Let F : R → R³ be a…

A: We know that  w × (v × u) =(w.u)v - (w.v)u div(curl F) = 0  And curl(gard f) = 0

Q: Prove the identity V x (V x F) = V(V · F) – V²F, where F is a vector field.

A:

Q: Sketch the following vector fields (at least 10 vectors) (a) F(x, y) =

A: Consider the provided question, 7 (a)

Q: Sketch the following vector fields:

A: given vector field is                                                       x-y, -x2

Q: Let A = (A, A,y, A2) and B = (B,, By, B2) be two arbitrary vector fields, prove the following…

A:

Q: Given the vector field F answer the following 个↑↑↑ 2.5 0.5 7 1 1 </ - گے۔ دوا د1 ۷۷ The curl( F…

A: To Determine: Sign of Curl and divergence at (2.5,2).

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 3. Is the series n=1 2n convergent or divergent? Hint: quotient…

A: The given series is .

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.