Find the divergence and rotation of the following vector A=i(x^2+y^2)+j(y^2+zx)+k(z^2+xy)

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: Given the matrix 3. 4 6 -7 Find the Characteristic Equation and find its solutions (aka:…

A:

Q: Consider the vectors A = (-5.4, 8.8) and B = (8.7, -9.4), such that A - B + 3.8C = 0   What is the x…

A: Let the coordinates for point C be (x, y).For the given coordinates of A and B, vector…

Q: Consider a rectangular surface of length L and width W in the xy plane with its center at the…

A:

Q: Given a space curve C with position vector 3 cos 2t i + 3 sin 2t j + (8t – 4)k r Find a unit tangent…

A:

Q: Find the Miller Indices of a plane whose intercepts are (2,1,3).

A: Given intercepts are (p,q,r)= (2,1,3) The Miller indices of a plane is    h,k,l=1p,1q,1r…

Q: prove that [L2,Lz]=0

A: L^2 is an operator that represents the square of angular momentumIt is equivalent toL^2 = L^x2 +…

Q: Consider the curve described by the parametric equations E = 2 cos t, y = 3 sin t For which value of…

A:

Q: Find the general solution of the given differential equation that is valid in any interval not…

A: Given, x2y''-3xy'+4y=0 ___(1) To find general solution of the equation

Q: A triangle in the xy plane is defined with = (0,0), (0, 2) and corners at (x,y) (4, 2). We want to…

A: The triangle has corners at (x,y)=(0,0), (0,2) and (4,2). We have a function f(x,y) which we need to…

Q: Let f(x)= 4xex - sin(5x). Find the third derivative of this function. Note ex is denoted as e^x…

A:

Q: Given the following matrix 3 3 1 5 Find its two eigenvectors. (A 3 and H2 0. B 3 and A, !! R -3 and…

A:

Q: Show that the force vector B = 2î – 4ĵ + k is orthogonal to the force vector ở = 3î + 43 + 10k. [2]

A: There are Two vectors -

Q: Consider the vectors A = (-8.1,5.4) and B = (10.7,-9.1), such that A - B +2.7C = 0. %3D

A:

Q: Let P:(-1,2,3), Pa(2,-1,1) and Pa(1,1,1) area of the triangle equal..

A:

Q: du (a) Let u be a differentiable vector function of constant length, then show that u. = 0. dt

A: Note: As per Bartleyby's guideline one question has to be solved at a time. So, upload other…

Q: Let f(x) = 4xe- sin(5x). Find the third derivative of this function. Note e* is denoted as e^x…

A: Derivative of two multiplicative function is given as  (fg)′=f′g+fg′

Q: Let A=5i-6.5 and B=3.5i-7ĵ . If lies in the xy-plane, Cis perpendicular to À , and Č-B=15 , what is…

A:

Q: prove that A ⊕ B Equal to inverse of Y= ĀB+AB̄

A: A xor B is given by A' B + AB' Given, Y = A' B + AB' Y' = (A' B + AB') ' Y'  = (A'B) '. (AB')'  Y' =…

Q: Suppose the vectors i, j, pand q are all unit vectors and the angle 0 = 340°. Find the cartesian…

A:

Q: Let vector A  point from the origin into the second quadrant of the xy plane and vector B point from…

A: When subtracting vectors, the rule is to graph the first two from the origin and then connect them…

Q: Let C be the plane curve given parametrically by the equations : x(t) = t² - t and y(t) = t² + 2t -…

A:

Q: 1. Defermine directional derivative of z= x-2yat the point (3,2,1) in the direction of0=4. 2.…

A: The directional derivative of a function z=fx,y along the direction of a vector v→…

Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (5,…

A: Vertices of rectangle: A(5,6), B(8,12), C(-40,36), D(-43,30)  When we'll plot these vertices on…

Q: Suppose the vectors i, j,pand q are all unit vectors and the angle 0 = 131°. Find the cartesian…

A: Required : The force in p and q coordinates.

Q: nates of point N. 2) Write the vector KM in terms o

A:

Q: Find the simplest SI unit of z, if Z = Fr³r? m³v²

A: Write the given values of this problem.  Let, F=force (kg.m/s2)r=radius mt=time secm=mass…

Q: Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there…

A: Let’s consider the following sets of vectors,

Q: Find the cross product A x C for (a) A = 2.0i – 4.0j +k and C = 3.0i + 4.0j + 10.0k, (b) A = 3.0i =…

A:

Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

A:

Q: Prove that AB, C -{ÂB‚C} + ({‚ĉ} - [A,C))B = 0, given that the commutator of X and Ý is denoted X,…

A:

Q: Which of the following is the conserved quantity if the system having Lagrangian L= = m(x² + y²) – ²…

A:

Q: P-1 Show the given set of function is orthogonal and find the Norm of the function in given set {cos…

A:

Q: Prove the relationship fP, >=<- dt

A: Prove the relation : ddt&lt;Px&gt;=&lt;-∂U∂x&gt;

Q: Find D in cartesian coordinates) at P(6,8,-10) caused by a uniforms surfacecharge density p,…

A:

Q: Consider the following scalar and vectors: Ã = 41+ 3) + 7k T = 3x+8yz + 2zx 1. Calculate for the…

A: REQUIRED  LAPLACIAN. DIVERGENCE.

Q: Given M = 6 î + 5 j – 6 k and N = 3 î - 3 j – 3 k, calculate the vector product M x N.

A:

Q: prove that F(x, y, z) = (3x² + .

A: Solution:

Q: Consider the curve described by the parametric equations x =t+ cos t, y = 2 – sin t. Compute the…

A: Slope or tangent to a curve in  X-Y plane is given as dY/dX.

Q: Find each of the following in rectangular (a + bi) form if z = 2 – 3i; if z = x + iy. 22.

A: Given that  and we have to solve for

Q: . Using the differential length dl, find the length of each of the following segments/curves: a) 2 <…

A:

Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…

Q: Find the real component if the complex number a + bi is raised to m if a = 7.4, b = 4, and m = 5.

A: Complex number form= a+biGivena=7b=4m=5