### Vectors

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

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

If v=3i-4j, find ||v||

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

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.

(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.

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

An object of weight 20kN is supported from above by two cables inclined at 40 and 70 degrees to the horizontal as shown (please see attachment)

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

1) A river 35 m wide flows south at a speed if 15 m/s. What must be the velocity and heading of the boat if it is to move directly from the west bank to the east bank in 5 seconds? 2) Two tractors are hooked to a combine. the combine needs to be pulled due east at 400 N. One tractor is pulling at 190 N, 32degrees S of

Three horses exert forces on a hitching pole. What is the resultant force on the pole, if horse A exerts a force of 350 N at an angle of 48 degrees N of East, horse B exerts a force of 560 N at an angle of 37 degrees N of West, and horse C exerts a force of 200 N at an angle of 87 degrees N of East?

1) What is the effective force acting to push a 57lb object up a 35 degree slope? 2) A person walks 450 feet at an angle of 53 degrees N of W. How far is the displacement west and how far north?

A person walks 18m East and then 32m in a direction of 65 degrees N of E. What is the resultant displacement?

A force of 25 N acts perpendicular to another force of 22 N. If the forces act together on the same object, what is the resultant force?

A person pushes with a force directed along the lawn mower handle, which makes an angle of 52 degrees with the ground. What must be the magnitude of the person's force in order to produce a horizontal force of 35 lbs?

A rope is wrapped around a pole so that a force of 75 lbs acts on one end and a force of 53 lbs acts on the other end. If the angle between the two forces is 114 degrees what is the resultant force? What angle does the resultant force make with the 53 lbs force?

Let G be a graph in which every vertex has degree 2. Is G necessarily a cycle? *Please see attachment for additional information. Thanks. Use words to describe solution process. Use math symbol editor like LateX, please no stuff like <=.

Let [a,b] be an interval in {see attachment}. Recall that the set of functions {see attachment} is a vector space over {see attachment} with addition (f+g)(x):=f(x)+g(x) and scalar multiplication a) choose [a,b]=[0,1]. Decide for each of the following subsets if it is a subspace. Justify your answer by giving a proof or a c

The diagram attached shows a rectangular solid, two of whose vertices are A=(0,0,0) and G=(4,6,3). a) Find vector projections of AG onto the following vectors: AB, [0,1,0], [-1,0,0] and [0,0,1]. b) Find the point on AC that is closest to the midpoint of GH (The diagram is on page 21 and it is problem 6) (As you can see

Please see attachment. Require problems solving, also explanations etc for better understanding of vectors. VECTOR PROBLEMS (1) Let l be the line with equation v = a + t u. Show that the shortest distance from the origin to l can be written | a × u |

Please see the attached file for full problem description. 1. Demonstrate (check the properties) that the following function is an inner product in R^3. (Call R^3 with this inner product Moorean 3-space). Let u=(u_1,u_2,u_3) and v=(v_1,v_2,v_3). Then <u, v> = uAv^T, where A=[ 2 0 0 ]

Please see the attached file for the full problem description. 1. Find the rank of A= [1 0 2 0] [ 4 0 3 0] [ 5 0 -1 0] [ 2 -3 1 1] . Show work. Help:

(1) a. Find the (vector) equation of the plane passing through the points (1,2,-2), (-1,1,-9), (2,-2,-12). b. Find the (vector) equation of the plane containing (1,2,-1) and perpendicular to (3,-1,2). (2) Suppose a, b, c are non zero vectors. a. Explain why (a x b) x (a x c)

Let V= (x,y) in R2{y=3x+1} with addition and multiplication by a scalar defined on V by: (x,y)+ (x',y')= (x+x',y+y'-1) k(x,y)=(kx,k(y-1)+1) Given that with these definitions, V satisfies vector space axioms 1,2,3,6,8,9,and 10 determine whether or not V is a vector space by checking to see if axioms 4,5,7,are also satisfied.