Algebra

See attached files

MA1310:

W

eek 7

S

olving Vectors

This lab requires you to:

· Use magnitude and direction to show vectors are equal.

· Visualize scalar multiplication, vector addition, and vector subtraction as geometric vectors.

· Represent vectors in the rectangular coordinate system.

· Perform operations with vectors in terms of i and j.

· Find the unit vector in the direction of v.

· Write a vector in terms of its magnitude and direction.

· Solve applied problems involving vectors.

· Find the dot product of two vectors.

· Find the angle between two vectors.

· Use the dot product to determine if two vectors are orthogonal.

Answer the following questions to complete this lab:

1. What is a directed line segment?

2. What are equal vectors?

3. Let v be a vector from initial point P1 = (–11, –12) to terminal point P2 = (2, 5). Write v in terms of i and j.

4. Let u = 8i – 6j and v = –5i + 8j. Find the vector u + v.

5. Find the unit vector that has the same direction as the vector v = –12j.

6. A Boeing 737 aircraft maintains a constant speed of 500 miles per hour headed due south. The jet stream is 80 miles per hour in the northeasterly direction.

a.

E

xpress the velocity va of the 737 relative to the air, and the velocity

vw

of the jet stream in terms of i and j.

b. Find the velocity vg of the 737 relative to the ground. (Hint: vg = va + vw)

c. Find the actual speed of the 737 relative to the ground. (Hint: )

E
W

N

S

vw = velocity of jet stream

vg

va = –500j

7.

The components of v = 260i + 300j

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represent the respective number of gallons of regular and premium gas sold at a gas station. The components of w = 2.50i + 2.65j represent the respective prices per gallon for each kind of gas. Find the dot product and describe what the answer means in practical terms.

8.

A force of 80 pounds on a rope is used to pull a box up a ramp inclined at 100 from the horizontal. The rope forms an angle of 330 with the horizontal. How much work is done pulling the box 25 feet along the ramp?

Definition of work: W =

Submission Requirements: Answer all the questions included in the lab. You can submit your answers in a Microsoft Word document, or write your answers on paper and then scan and submit the paper. Name the file as InitialName_LastName_Lab7.1_Date.

Evaluation Criteria:

· Did you show the appropriate steps to solve the given problems?

· Did you support your answers with appropriate rationale wherever applicable?

· Were the answers submitted in an organized fashion that was legible and easy to follow?

· Were the answers correct?

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*
vw

Vectors are a profound invention. In science and technology, they provide a simple model for visualizing difficult concepts such as force, velocity, and electric fields. Vectors are essential to creating today’s amazing computer graphics.

Dot product of vectors is an operation on vectors. Some of the applications of dot product are in solar energy, physics, and computer graphics.

A few specific examples are:•Measuring rainfall

•Finding the braking load of a car from rolling down a hill at an angle

•Finding the force required to hold a wagon on a hill

•Finding an angle of a ramp to load furniture or other articles into a truck

•Air navigation—finding groundspeed and direction of an airplane in the wind

•Finding speed and direction of a swimmer when swimming in a river with current

You are required to:•Pick a real-life application in which dot product of vector is used.

•Describe the application in a paragraph of at least 100 words.

•State which branch of science/engineering this application belongs.

•Write the question posed in the application that needs to be solved.

•Execute the dot product to solve the question posed.