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Vector Calculus

VECTOR

FIND THE HORIZONTAL AND VERTICLE COMPONENTS OF THE FOLLOWING FORCES:(237LBS, 48 DEGREES),(369LBS,248 DEGREES) ALSO FIND THE X AND Y COMPONENTS OF THE VECTOR (529m,342DEGREES)

What is the resultant force?

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?

Vectors

What is the resultant force for the following forces? 250 N due north, 525 N due south and 238 N 38 degrees south of west.

Vectors

Find the force on the docking cable of a boat on which the wind acts in a northerly direction with a force of 235 lbs and the tide acts in an easterly direction with a force of 323 lbs.

Vectors

A block of wood weighing 35 lbs is resting on an inclined plane sloped at 36 degrees to the floor. What is the component of weight down the plane? What is the component of weight perpendicular to the plane?

Vector Components : Weight

A 850 LB PULL ACTS IN A DIRECTION 32 DEGREES S OF E. WHAT IS THE EASTWARD COMPONENT? WHAT IS THE SOUTHWARD COMPONENT?

Vector Fields

Let a vector field F be given by F(x,y,z) = (x^3)i - (y^2)j + (2yz)k and a curve C be given by r(t) = 2ti + sintj - costk, 0 <= t <= (pi/2) 1. Evaluate the line integral F*dr. 2. Determine the arclength variable s from t. 3. Determine the unit tangent vector T(s). 4. Evaluate the total arclength L. 5. Write th

Trees: Vertex; Cycle

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 <=.

Strictly separating sets

For both 1 and 2, could you tell me whether or not there is a hyperplane that strictly separates the given sets A,B. If there is, find one. If there is not, prove so please. 1) A={(x,y):abs(x) + abs(y) <=1}, B={(1,1)} 2) A={(x,y):xy >= 4}, B={(x,y):x^2+y^2 <= 1} where abs = absolute value

Linear Algrebra - Vectors in R^n, Orthogonal Spaces and Lines of Best Fit

1) Let u and v be vectors in R^n. a) Prove that llull = llvll if and only if u + v and u - v are orthogonal. b)Let (proj of u onto v) be the vector projection of u onto v. For u, v does not equal to 0, prove that (projection of u onto v - u) is orthogonal. 2) Find a basis for the space orthogonal to [1,1,0]^T in R^3.

Mechanics: Scalar and Vectors

1. Given the following 3 vectors, all of which lie in the horizontal plane, (see attachment for list of vectors), find: (a) 3A-B (b) 1) A?B 2) B?A (c) 1) A*B 2) B*A (d) (5A-6B+4C)?(B*C-A*B) *(Please see attachment for complete question and equations)

Properties of vector spaces.

Which of the following are subspaces of the vector space ? Justify your answer. A vector space in R^3 such that every vector (a,b,c) has the property: a-b-c=2 A vector space in R^3 which has the form (a,b,a+b)

Subspace

If U is a subspace of V then W=V-U (a vector x that belongs to W can not belong to U) W also is a subspace. (Proof or counterexample)

Determine a normal vector to this surface at the point...

Let X: R^2 &#61664; R^3 be the parameterized surface give by X(s,t) = (s^2 - t^2 , s + t, s^2 + 3t) A) Determine a normal vector to this surface at the point (3, 1, 1) = X(2, -1) b) Find an equation for the plane tangent to this surface at the point (3, 1, 1)

Vectors

Could you please give me some sort of a sketch or drawing of what a set S (its interior and its closure) would look like when: S= {(x,y) : -1<= y < cosx, -2# < x <= 2#} Note: <= is less than or equal to < is less than # is pi (3.14....)

Vector Subspaces

What would a vector v in R4 such that: V(1,2,1,0) T V(1,0,-1,1) T V(0,2,0,-1) = <v> AND find scalars a,b,c,d such that <(1,2,1,0),(1,0,-1,1),(0,2,0,-1)> = <v> Please note: <v1,...,vk> denotes the vector subspace of Rn generated by the vectors v1,...,vk and that for scalars a1,...,an belonging to R, V(a1,...,an) =

Vector projection and follow-up

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

Vector : Gradient

The temperature of a plate at the point (x,y) is given by T(x,y) = 300+ 3x^2 -2y^2. A heat hating ant is located at the point (3,2). In which direction will the ant begin to walk? Give a unit vector in that direction.

Multivariable Calculus : Double Integral - Polar Coordinate

( ∫ ^n_r means that n is on the top of the ∫ and r is on the bottom) Evaluate the given integral by first converting to polar coordinates: ∫ ^2_1 ∫ ^(square root of 2x - x^2)_0 (1/(square root of x^2 + y^2)) dy dx ∫: is the integral symbol

Vectors

The set of vectors {[ 1 -1] , [ 1 -1] , [ 2 -1] } [ 2 0 ] [ -1 0] [ -1 0] from M_2(R) is: A. linearly dependent B. linearly independent C. orthogonal D. a spanning set for M_2(R) E. a basis for M_2(R)

Vectors

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 |

Vector operations please check this for me thanks

Given vector v with /v/ = 4 and direction angle of 45 degrees, write v in the form <a,b> a= 4cos 45 degrees= 4*.707=2.83 b= 4sin 45 degrees= 4*.707=2.83 vector v (a,b) becomes v(2.83, 2.83) compute (2*w).(u-v) where w = <-1, 0> 2(2<100)(5<60-4<45) 2*2<180*1.536<102.5 =6.144<282.5 or 6.144<-77.5degrees vector from equat