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Vector Calculus

Parallel and Perpendicular Vectors and Work

1 Given a = 9i - 5j and b = 7i-4j, express i and j in terms of a and b 2 Given a=<4,5,-3> and b =<4,-2,2> determine whether a and b are parrallel, perpendicular, or neither. 3 Given F = 4i -2k;..... P(0,1,0) and Q(4,0,1) find the work W done by the force (F)moving a particle in a straight line from P to Q. 4 Given a

Express each vector as linear combination of basis.

Find a subset of the vectors that forms a basis for the span of the vectors; then express each vector which is not in basis as a linear combination of the basis vectors. v1= (1, 1, -1), v2= ( 1, 0, 1), v3= ( 1, -2, 5), v4= ( 5, 3, 2)


1. Find the component form of the vector representing the velocity of a boat traveling at 8 knots, or nautical miles per hour, with a bearing of N 53-degrees W. 2. A force of 703 pounds is needed to push a stalled car up a hill inclined at an angle of 16-degrees to the horizontal. Find the weight of the car. Ignore fric

Vector-valued function word problem

A baseball is hit from a height of 3 feet with an initial speed of 120 feet per second at an angle of 30 degrees above the horizon. Find the vector-valued function describing the position of the ball t seconds after it is hit. To be a home run, the ball must clear a wall 385 feet away and 6 feet tall. Determine if this is a home

Problems Related to Vectos: Force, Motion, and Currents

Please explain in step by step detail the following: 25. A weight of 850 pounds is suspended by two cables. One cable makes an angle of 66 degrees with a vertical line, the other makes an angle of 42 degrees with a vertical line. Find the amount of force exerted by each of the cables. 24. An airplane is scheduled to reach

Vectors in spherical and cylindrical

(a) Given A = a*p_hat + b*psi_hat + c*z_hat (cylindrical unit vectors), where a, b, and c are constants. Is A a constant vector (uniform vector field)? If not, find: the divergence and curl of A (b) If A = a*r_hat + b*theta_hat + c*phi_hat in spherical coordinates, with constant coefficients. Is A a constant vector (unifor

Vector Spaces

How to prove or counter with example the following statements: (1) If two subspaces are orthogonal, then they are independent. (2) If two subspaces are independent, then they are orthogonal. I know that a vector v element of V is orthogonal to a subspace W element V if v is orthogonal to every w element W. Two subspaces W1

Proof of Vertex, Extreme Point, Basic Feasible Solution

Can you please let me know how to approach those proof questions. Consider the polyhedron P = {x &#61646; Rn : xi > 0 for all i = 1 ... n}. a)Prove that the origin (i.e. the vector of all 0's) is a vertex of P, according to the definition of a vertex (i.e. do not rely on the fact that vertex = extreme point = basic feasibl


Using the given vectors how do I find the specified dot product u=3i-8j;v=4i+9j find u.v

Vector Field, Gradients, Div, Divergence, Curl and Surface Integrals

4) A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P1 and P2 a.) Are the points P1 and P2 so sources or sinks vector field F shown in the figure? Give an explanation based solely on the picture. 5)Use the divergence Theorem to c

Potential and Electric Field Vector of Two Concentric Charged Cylinders

B. A region is surrounded by two infinitely long concentric cylinders of radii, a1 and a2 (a2>a1). The concentric cylinders are charged to potentials phi1 and phi2 respectively. Determine the potential and electric field vector everywhere in the region. Please see the attached file for the fully formatted problem.

Vector Calculus

Hi, I cannot figure this problem out. I would like to see how to work it. The answer in the book is 3/e, but I cannot get it. There must be a trick involved (hence the author's hint to think carefully), but I'm not sure what it is. I attached the problem. Thanks

Vector Calculus : Flux and Gauss's Law

(a) Consider a vector function with the properly ... = 0 everywhere on two closed surfaces S1 und S2 and in the volume V enclosed by them (see the figure). Show that the flux ol F through S1, equals the flux of F through S2. In calculating the fluxes, choose the direction of the normals as indicated by the arrows in the figure.

Vector Calculus - Flux and Magnetic Fields

(a) One of Maxwell's equations states that V H = 0, where 11 is any magnetic field. Show that if...for any closed surface S. (b) Determine the flux of a uniform magnetic field B throngh the curved surface of a right circular cone (radius R, height h) oriented so that B is normall to the base of the cone as shown in the figure.

Velocity/position vectors

Given that the acceleration vector is a(t) = (-9cos(-3t)) i + (-9sin(-3t)) j + (-2t) k , the initial velocity is v(0) = i + k , and the initial position vector is r(0) = i+j+k , compute: A. The velocity vector B. The position vector

Hilbert Space and Subspace

Problem. Show that if is an orthonormal set in a Hilbert space H, then the set of all vectors of the form is a subspace of H. Hint: Take a Cauchy sequence , where . Set and show that is a Cauchy sequence in . Please see the attached file for full problem description.

Gradients : Elliptic Paraboloid and Vector Fields

Please see the attached file for the fully formatted problems. Suppose that a mountain has the shape of an elliptic paraboloid , where a and c are constants, x and y are the east-west and north-south map coordinates and z is the altitude above the sea level (x,y,z are measured all in metres). At the point (1,1), in what direc