Vectors

1) Both vectors A and B have a magnitude 5 and the angle between them is 53.13 degrees. Calculate the magnitude of A+B.

2) The diagram shows vector C. Determine the X and Y components of C.

see attached file for details

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 |
――――
| u |

(2) Two planes having equations r . n1 = λ1 and r . n2 = λ2 intersect in the line l.

Show that a = (n1 × n2) × (λ2 n1 – λ1 n2 )
――――――――――― is a point on l.
| n1 × n2 |²

Hence find the point where the three planes

r . n1 = λ1 , r . n2 = λ2 , r . n3 = λ3 .

(Assume that the planes do intersect in a point).

Vectors

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 east. What angle and force must the second tractor be doing?

Vectors

Please give step by step answers with solutions details please. I learn by seeing things done. Thank you!

Their are 3 attachments.

Vectors

What is the resultant force of an object if there are forces of 70 lbs at an angle 90 degrees N of west, 55lbs at an angle of 63 degrees S of west, and 42 lbs at an angle of 158 degrees N of east?

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?

Vectors

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

Vectors

If A=(12i-16j) and B=(-24i+10j),what is the magnitude of vector C=(2A-B)?

Vectors

Suppose we want to find out whether the set of vectors { v1, v2, v3 } is linearly independent or dependent.

1. Write the vector equation to be solved.

2. Write the vector equation as a linear system.

3. Write the augmented matrix of the linear system.

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

Three vectors have the same length (L) and form an equilateral triangle. Find the magnitude and direction of the vectors:
(a)A+B
(b)A-B
(c)A+B+C
(d)A+B-C.

Please see attachment below for figure.

Vectors

Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in length and points along the negative y-axis. Use the graphical methods to find the magnitude and direction of the following vector:
B.) A+B

The work I need to show to complete this problem is a free body diagram, formulas, work w/units and answer w/unit if possible.

Vectors

You are given the vectors
X = (1,1,1), y = (2,1,1) and z = (6,2,2).

(i) Find the Cartesian equation of the plane Π normal to the vector x containing the point (2,1,1).

(ii) Find the parametric equation of the line l through the points (2,1,1) and (6,2,2).

(iii) If l’ is given parametrically by l’ = x + ty (with x and y defined above), find the point of intersection of l’ with the plane Π.

(iv) Find x x y, y x z and [x, y, z].

Give an explanation in geometric terms of what you have found.

Vectors

1. Find the angle between the planes with the given equations.

2x – y + z = 5 and x + y – z = 1

2. Find the values of r’ (t) and r” (t) for the given values of t.

r (t) = i cos t + j sin t; t = pi/4

3. The acceleration vector a (t), the initial position r = r (0), and the initial velocity v = v (0) of a particle moving in
xyz-space are given. Find its position vector r (t) at time t.

a(t) = 6ti – 5j + 12t²k; r = 3i + 4j; v = 4j – 5k

4. Find the curvature of the given plane curve at the indicated point.

10. x = t – 1, y = t² + 3t + 2, where t = 2

5. Find the unit tangent and normal vectors at the indicated point.

18. x = t³, y = t² at (-1, 1)

Vectors

Suppose A(3,-1,0) and B(-4,-2,3) are 2 points in 3-space. Find a vector with the following three characteristics: initial point at the origin, collinear but in the opposite direction of vector AB , length 3

Vectors

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^2 such that each entry of e is equal to 1. Show that

(u-a e).(v-b v)=u.v – (n^2 a b)

NOTE: The textbook is “Image Based Information Processing”

Vectors

Briefly describe the purpose of the following features found in all or many plasmid cloning vectors.

a) origin of replication (ori)
b) multiple cloning site (polylinker)
c) antibiotic resistane gene

Vectors

1. Two vectors are parallel provided that one is a scalar multiple of the other. Determine whether the vectors a and b are parallel, perpendicular, or neither.

a = 12i – 20j + 17k and b = -9i + 15j + 24k

2. Find a unit vector n perpendicular to the plane through the points P(1, 3, -2), Q(2, 4, 5), and R(-3, -2, 2). Then find the distance from the origin to this plane by computing n ? OP.

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 friction.

3. The vectors U and V are orthogonal. Find the value of a.
U= {a,-7}, v= {42,-30}

4. A horizontal force of 80 pounds is applied to an object as it is pushed up a ramp that is 13 feet long. Find the work done if the ramp is inclined at an angle of 40-degrees above the horizontal.

5. Find the indicated roots of the complex number. Fifth roots of 32.

Vectors

A rocket in outer space that is moving at a speed of 1.50 km/s relative to an observer fires its motor. Hot gases are expelled out the rear at 2.55 km/s relative to the rocket. What is the speed of the gases relative to the observer?

Vectors

Let u and v be vectors in an inner product space V such that ||u + v|| = 4,||u – v|| = 1 and ||v|| = 2. Calculate the value of ||u||.

vectors

The eastward component of vector A is equal to the westward component of vector B and their northward components are equal. Which one of the following statements is correct for these two vectors?

Choices:

Vector A is parallel to vector B
Vector A is anti-parallel to vector B
The magnitude of vector A is equal to the magnitude of vector B
The magnitude of vector A is twice the magnitude of vector B