Show that the order of addition of three vectors does notaffect their sum. Show this property by choosing any threevectors A , B , and C , all having different lengths anddirections. Find the sum A + B + C then find their sumwhen added in a different order and show the result is thesame. (There are five other orders in which A , B , and Ccan be added; choose only one.)

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Plane passing through the point (0,2,-3) and with normal vector 4i - j -2k means perpendicular to…

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: Answer 5,6,7,8,9 write whether attract or repel for every number

A: As we know that that  same pole repels and opposite poles attract i.e, N pole  will  repel N pole…

Q: * the prime Gordinates system C is obtai nal by rotating the C system throtigh ans angle 60° axis…

A:

Q: find the angle between two vectors, 6 and 8units long, when their is 10 units long and 4 units long

A: Use cosine theorem When 10 units long a = 6 , b = 8 and c= 10 (10)2  = (6)2 + (8)2 + 2×6×8 cosA  100…

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 n = VE,

A: given data :-

Q: Evaluate the given integral. Jx²Inxdx

A:

Q: Prove that I de xR

A:

Q: Th unit vector from the origin {i.e. the point (0,0)} to the point B (3,4) is:

A:

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: Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }

A: To solve the given question, we will write down the given two vectors in vector form and then we…

Q: Show that for orthogonal coordinate systems gij= 0 for i not equal to j

A:

Q: Show that if a matrix is orthogonal and its determinant is +1, then each element of the matrix is…

A: Let A is an orthogonal matrix with determinant equal to+1. Orthogonal matrix, AAT=1…

Q: Consider the following Hermitian matrix 3 1 i 2 1i a) find the eigenvalues find the eigenvectors b)…

A: (a)The eigen values is,

Q: Prove that

A: To prove: It is known that:

Q: A docs.google.com/forms/d/e Which function is preferable to find the magnitude of a complex number?…

A: 1. Correct option is : abs ()

Q: Evaluate the surface integral /| (2xzdydz + ydzdx + z?dxdy) where S is a closed surface, given by S:…

A: Given:I = ∯S 2 xz dy dz + y x dx dz+…

Q: For any two vectors A and B, if A.B =0 then the angle between them is Zero aO degree 90.b O degree…

A: Given here for two vectors A and B if A→. B→ =0we are asked what is the angle between vector A and…

Q: Find the angle vector c makes with the +x axis. 10 10 Hint: Use inverse trig function, carefully.

A: We have to find the angle vector c makes with the +x axis. We can use inverse the trigonometric…

Q: (Vector analysis) Given the function v with cubic volume having sides of length 2 from the origin as…

A:

Q: If f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇f

A:

Q: Which of the following is the conserved quantity if the system having Lagrangian - m. (а) Р, (b) Р,…

A:

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 that you have two vectors (1,0,0, 1) (2,0,0, 2) at What is a"b,?

A: Given that aμ=(1,0,0,1) and bμ=(2,0,0,2) we have to find the value of aμbμ

Q: Derive the matrix for rotation around the x-axis 30

A: Basics of Rotation matrix: Rotation matrix is  used to perform a rotation in Euclidean space. The…

Q: In the graph given below, at the point B, the nature of gradient (dy/dr) is A 4

A: Ans : b) zero

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 centroid of the region bounded by the set of curves

A: Area Bounded by the Curves:When area bounded by curve and line has to be identified, then the…

Q: Consider a cube with one corner at origin and the other corner along the body diagonal at (1,1,1).…

A:

Q: prove thar the volume of the parallele piped with adjacent sides vectors A. B and C is egqual

A:

Q: If F = (2x2 - 3:) î – 2xy j - 4xk, then evaluate , V F dV, where V is bounded by 1. x = 0, y = 0, z…

A:

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

A:

Q: Which of the following is the conserved quantity if the system having Lagrangian 1 (а) Р. (b) Р, (c)…

A: Lagrangian of a system is a function of generalised coordinate, first derivative of this generalised…

Q: Evaluate the integral W = mv dv. %3D Express your answer in terms of m, vj, and vf.

A: Part F: The given equation of work in the integral form is: W=∫vivfmvdv

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: Q.1CC)IFE igen value of matrix is d, the corresponding eigen for matrix -882 vector is Lil 32 then d…

A: Given: The matrix is given as Let X be the Eigenvector matrix.

Q: No matter what A and B, prove algebraically that A(A×B)=0

A: The vector C, C→=A→×B→=AB sinθ n^   Here, vector C is perpendicular to vector A and vector B.

Q: Without finding T and N, write the

A: position vector r is given. want to calculate acceleration. acceleration =ddt(drdt)

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: ) Show that the curl of (b x7) is 2b. Where i is the position vector

A:

Q: If the vector A(x,y,z) is perpendicular to the closed surface S prove that: where T is the volume…

A:

Q: Let vectors A=(2,1,−4), B=(−3,0,1), and C=(−1,−1,2).Calculate the following: What is the angle θAB…

A: Given,

Q: Realize Stoke's theorem for vector (A=jx+ky) and for a square whose area is one unit in the plane…

A: