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# Vector Calculus

### Vector Subspaces, Gram-Schmidt and Orthogonal Basis

1) Find the closest point to y in the subspace W spanned by v1 and v2. y= v1= v2= #2) Let y, v1, and v2 be as in exercise #1. Find the distance from y to the subspace of R4 spanned by v1 and v2. #3) The given set is a basis for a subspace W. Use the Gram-Schmidt process to produce an orthogonal bas

### Explain why vectors QR and RQ are not equivalent.

The "blog" has been quiet for a while, so you decide to create a math challenge. You post the following issues and then try to address them along with the people you've been interviewing. Explain why vectors QR and RQ are not equivalent. Explain in your own words when the elimination method for solving a system of equations

### Parabola

Write an equation for the parabola Vertex(-2,1) and focus (-2,-3)

### Vertices in Tree

A tree has 11 vertices of degree 3, 12 vertices of degree 2, 10 vertices of degree 4 and the remaining vertices are of degree 1. How many vertices does it have?

### Vectors and Subspaces

2 a) Find a base for the subspace W of spanned by What is the dimension of W? b) Let 1) Show that W is a subspace of 2) Find a base for W 3) Determine the dimension of W c) Let 1) Determine whether Y is a base for , the vector space of all 2 x 2 matrices. d) Find the two values of a for which the

### Vector Spaces and Subspaces, Addition and Scalar Multiplication

Please view the attached files to see the expressions which are in question for parts A and B. 1. A) Determine whether the following sets are vector spaces, in each case giving reasons for your answer. B) Determine whether W is a subspace of the given vector space V.

### Equilibrium vector

Find the equilibrium vector for each matrix M1 = .85 .15 M2= 3/5 2/5 .55 .45 1/4 3/4

### Image Based Information Processing

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^

### Parallel 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.

### Finding center, vertex and directrix of parabola, ellipse, hyperbola

Please show in detail how to find the center, vertex, & directrix of parabola, the center, vertices, & foci for the ellipse, the center, vertices, foci, & asymptopes of any hyperbola 1) 9X^2+4y^2-18X-27=0 2) x^2+4X-8y+28=0 3) -3x^2+2y^2+12x-4y+8=0

### 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)

### Find the cross product and its magnitude of given vectors

Please find the 1) length and 2) direction (when defined) of 1) A X B and 2) B X A Please show all work, including the grids for the determinants. Thank you. A = 2i + 3j B = -i + j

### Vectors in the plane and the horizontal/vertical components of force : A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal.

Please find the horizontal and vertical components of F in the problem below: A kite string exerts a 12-lb pull (F=12) on a kite and makes a 45° angle with the horizontal. Find the horizontal and vertical components of F.

### Newtonian viscous flow equations - plane stagnation

Prescribed textbook: Viscous Fluid Flow, 2nd Edition, F. M. White In the attached document. Please show me in detail (use maths) how to obtain the equation 3-149 from 3-148 and how to obtain equation 3-151 from 3-150.

### Vectors

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

### Vectors : Arc length of a space curve

Use the integration capabilities of you graphing utility to approximate the arc length of the space curve given by: vector r(t) = t i + t^3 j + 3t K from the point (1,1,3) to the point (2,8,6). Round your answer to the nearest three decimal places. I did this problem and got the answer 2.003 X 10^10. Would you please show

### Unit Normal Vector Planes

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?

### Velocity, speed and acceleration of a vector-valued function

Find the velocity, speed and acceleration of the vector-valued function: Vector r = cost i + sint j - 16t^2 k at t=pi/4

### 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.

### 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

### Non-Equivalence of Vectors and Elimination Versus Substitution

1. Explain why vectors QR and RQ are not equivalent. 2. Explain in your own words when the elimination method for solving a system of equations is preferable to the substitution method.

### Parabolas: Concave Up or Down, Vertex and Intercepts

Given the parabola y = -(x - 6)2 - 1, determine each of the following. 7. Identify whether the parabola y = -(x - 6)2 - 1 opens up or down. 8. Identify the vertex of the parabola y = -(x - 6)2 - 1. 9. Identify the x-intercept(s) of the parabola y = -(x - 6)2 - 1. 10. Identify the y-intercept(s) of the parabola y

### General Vector Spaces

Question: Let W be the space spanned by f = sinx and g = cosx. (a) Show that for any value of theta, f, = sin(x + theta) and g_1 = cos (x + theta) vectors in W. (b) Show that f_1 and g_1 form a basis for W.

### 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

### Complex Inner Products and Orthonormal Sets

Let V be the vector space of all complex valued polynomials defined over the half line [0,infinity). (a) Show that <f,g> = &#8747; 0-->&#8734; f(x) ( g(x) bar) e^-x dx is a complex inner product on V g(x) bar is g(x) with a bar on it, which I believe to be the conjugate. (b) Find an orthonormal set : {f_o, f_1} in

### Vector Fields and Work Done when a Particle Moves Along a Curve

Given...determine if F is conservative. Find its potential. Given...find the potential of this conservative field. Find length of curve... Find curl F... Given the vector field... find work done when a paritcle moves along a curve. Please see the attached file for the fully formatted problems.

### Vector Calculus: The Geometry of Real-Valued Functions

Describe the surfaces in R3 of the equation: y^2 = x^2 + z^2.