show that velocity and acceleration are contravariant vectors and that the gradient of a scalar field is a covariant vector.

Q: Show that vector Å = 4î - ĵ + 2k and B = i+2 j- k are perpendicular. %3D

A:

Q: The unit vector from A(4, 2) to the point B(-2, 10) is:

A:

Q: 21-41+5k; i-mj+k, and 3 1 + 21-5k are coplanar_

A: In order to be coplanar vectors, their scalar tripple product must be zero. We can find scalar…

Q: A capacitor with an initial potential difference of 75 V is discharged through a resistor when a…

A: Given: In this question,  The capacitor with an initial potential difference , Vo=75V is discharged…

Q: A vector field is defined by:  F (x,y,z) = -xi - yj + zk  Select the option that gives F expressed…

A:

Q: Write the given vectors in terms of its components and the corresponding unit vector and then verify…

A:

Q: A charged particle is on an x-y plane. The particle starts from the origin, and begins by moving…

A:

Q: The magnitude of the x-component of a unit vector at the point (1, 1) that is normal to $(r) =,…

A: We can write the electric field as given by-…

Q: Consider the velocity field, V = (x² + y² − 4)i + (xy — y)j, where x and y are in m and V is in m/s.…

A: As per guidelines, We are supposed to answer one question from multiple questions kindly post other…

Q: LET U AND V BE SCALAR VECTOR FIELDS. PROVE: f₁ UVV.de=-f VVU.de L

A: To prove the identity: ∮U∇⋅V · dl→ = -∮V∇⋅U · dl→ where U and V are scalar vector fields, we will…

Q: Given the function D= 3x²y - y³z², find the gradient VQ. b. a. 6xyî+ (3x² - 3y²z²)ĵ- 2y³zk…

A: Given, Φ = 3x2y - y3z2

Q: Q3- (a) Show that for what values of X,Y and Z the transformation of A = is orthogonal and then show…

A:

Q: Find the equation of the perpendicular bisector of the line segment joining the points A(2, 3) and…

A:

Q: Determine the scalar components R, and R₂ of the force R along the nonrectangular axes a and b. Also…

A: Given that,  R = 760 N Angle, θ = 110° and Φ = 27° Another angle, q = 180° - (110° + 27°) => q =…

Q: The vectors ā, b and čare not planar. The a', & and d are the associated reciprocal vectors given by…

A:

Q: Four point charges (two with q = +2.5 × 10¬6 C and two with q = -2.5 × 10" C) are situated at the…

A: qA = 2.5×10-6C qC = - 2.5×10-6 C distance between A and C = 2 m

Q: Salt water with a density of 6 = 0.25 g/ cm flows over the curve r(t) = /5ti+ 2ij. Osts5, according…

A: Given: ς= 0.25 g/cm2 rt=5ti+2tj

Q: u and v are arbitrary vectors and A is an arbitrary tensor. Does A(u x v) = Auxv +ux Av?

A: Given:  u and v are arbitrary vectorsA is an arbitrary tensor.

Q: Transform each of the following vectors to spherical coordinates at the point specified. F = yax -…

A:

Q: Given A = a - a , B = 2a, and C =- a + 3a , find (A •B)× C y 5 Answer:

A:

Q: Check if the gradient theorem is fulfilled by integrating f = x2 + 4xy + 2yz3 between the points a =…

A:

Q: t systems. Wri

A: Given: To find the dynamic equations in the matrix form of vector is given using the transfer…

Q: H=ре салфар te'sing an tpar At point (1,5,6) find: a) H⋅ax b) H x do c) The vector component of H…

A: Given, H=ρzcosφaρ+e-2sinφ2aφ+ρ2az

Q: Find the divergence of the vector field. (V.V=V + OV₂ + 2/₂V₂) дх дz V(x, y, z) = (x²y, 3y, 5) =…

A:

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force triangles, to…

A: The orientation of the for 240 N from the positive x-axis is, The orientation of the for 180 N from…

Q: x²y°z* , e" sin(y) In(z). 2.3.4 g(x, y, z) = h(x, y, z)

A:

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: Express the vector field D = (x² + y²)−¹(xɑx + yay) in cylindrical components and cylindrical…

A: The cylindrical coordinates (ρ, ϕ, z) of a vector are related to its cartesian components (x, y, z)…

Q: Q. 9: Find the direction cosines of cartesian coordinates (4, -1, 2).

A:

Q: Given a vector field A = 5x ^ 2(sin (pi*x)/2) i, find V.A at x = 1

A: Vector A = 5x².(sin (pi.x)/2)i

Q: Calculate the commutators [^px2, ^x2].

A:

Q: How far did the boat travel from the point where the distress call was made to the point where the…

A:

Q: Describe 2-dimentional vector addition for any scenario? Put your bes example over here.

A: Vector addition in two dimension Let us consider two vectors A →and B→, such that they are oriented…

Q: A treasure map directs you to start at a palm tree and walk due north for 15.0 m. You are then to…

A:

Q: The resultant of two vectors is 20 units long and makes angles of 20o and 50o with the two vectors,…

A: Given, Length of resultant,R=20 units Angle of resultant with vectors,θ1=20°,θ2=50°

Q: (a) Let F₁ = x² 2 and F₂ = x Ŷ + y ŷ + z 2. Calculate the divergence and curl of F₁ and F₂. Which…

A: