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Vector Calculus

Vector problem

Each square n*n region of an image yields a vector of length n^2 such that the components of the vector are the grey levels of the pixels in the square. Let u, v be the vectors obtained from two image patches, let a be the average of the entries in u, let b be the average of the entries in V and let e be the vector of length n^

Vector Fields

(See attached files for full problem description) For this one you need chapter 2 I think, it is problem number 4 page 57.

Tangent and Normal Unit Vectors

Please show a detailed solution to this problem. Pleas show the curve and vectors together in a sketch. Thank you! Find the unit vectors that are tangent and normal to the curve at the given point: y = e^x , (ln2,2)


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

Unit Normal Vector

Let vector r(t) = t i + t^2 j represent a plane curve. Find T(t), T(1) and N(1). Sketch the plane curve and graph the vectors T(1) and N(1) at the point t = 1.

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

Unit tangent and unit normal vectors.

Given the vector r(t) = t i + t^2 j find T(t), T(1) a dn then N (1). After this I am to sketch the plane curve and graph the vectors T(1) and N(1) at t = 1.

Unit Tangent Vector

I am asked to find the unit tangent vector at t=2 for the following : vector r(t) = t i + t^3 j + 3t k How do I do this problem and what is the final answer?

Evaluating the limit of a vector.

How do I evaluate the limit of the following vector: lim[(e^2t/t^2-1)i + (1-cost/t)j + sq rt (4-t^2)] t-->0 How do I go about solving this problem and what is the answer that will be obtained. I'm not even certain where I should begin.

Please explain in step by step detail the following

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 reac

Vector-Valued Functions

The problem asks me to sketch the curve represented by the vector-valued function. The vector-valued function is: r(theta) = cos theta i + 3 sin theta j The solution in the solution manual has the following: x = cos theta y = 3 sin theta Up to here I understand what is being done. T

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

Three Ellipses and Completing the Square: Vertices, Foci and Eccentricity

1) 9x^2+4y^2+36x-24y+36=0 The answer is as following: Vertices: (-2,6), (-2,0) Foci: (-2, 3+or -√5) Eccentricity: √5/3 I have listed the answers for no. 1 above, but don't understand the steps. Please explain. 2) x^2+5y^2-8x-30y-39=0 Center: (4, 3) Vertices: (-6, 3), (14, 3) Foci: (4 + or -

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

Vector calculus: Flux and Surface Integral

#2) Flux integrals; s F?n dA. Evaluate the integral for the following data. Indicate the kind of surface. (show the details of your work): F=[x2, ey,1], S: x+y+z=1, x 0, y 0, z 0 Kreyszig's Advanced engineering mathmatics 8th ed.: section 9.6: Surface integrals Please s

Partial Order, Linear Functional, Vector Space and Subspace

Let be a vector space and a subset of such that implies and for Define a partial order on by defining to mean . A linear functional on is said to be positive (with respect to ) if for . Let be any subspace of with the property that for each there is an with . Assume that , where Then each positi

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  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

Area Measure and Orthogonal Vectors

Let m be an area measure on {z in C:|z| < 1}. Show that 1, z, z^2,... are orthogonal vectors in L^2(m). Find ||z^n||, n >= 0. If e_n=(z^n)/||z^n||, n >= 0, is {e_0, e_1,...} a basis for L^2(m)?

Position vector

The vector v has an initial point p of (7,3) and terminal point q of (-5,-4). How do I find its position vector and write v in the form of ai + bj?