Vectors
Linear Dependence and Coplanarity
GO TO: THE DROPBOX AND UPLOAD YOUR WORK.
MCV4U d1+ B – Linear Dependence and Coplanarity Assignment
Answer all questions with full solutions. Make sure your work is legible, even after you have
scanned it, and submit it as a single file.
1. Write an example of each of the following (assuming it is in 3dimensional space).
a. A point lying on the xaxis.
b. A point lying on the yz plane.
c. A point lying on both the xy and xz planes.
d. A point lying on all three planes.
e. A point lying on none of the three planes, but equidistant from the xz and yz planes.
2. Triangle ABC has vertices A (1, 1, 3), B (1, 3, 5) and C (3, 3, 3). What kind of triangle is ABC
Justify your answer.
3. The points (1, 2, 4), (3, 5, 7) and (4, 6, 8) are three of four vertices of parallelogram ABCD.
Explain why there are three possibilities for the location of the fourth vertex, and find the three
points.
4. The points A (3, 1, z) B (1, 2, 6) and C (x, 8, 14) are collinear. Find the values of x and z.
5. Explain the meaning of direction angles and their relation to direction vectors.
a. What are the direction angles of the vector [2, 4, 3]
b. If a point P lies on the xaxis, what are the direction angles of the position vector
OP
c. Prove that
2 2 2 cos cos cos 1
d. A vector has direction angles a = 75° and ß= 55°
i. Find the value of
ii. Find a vector that has those direction angles
e. Explain why it is not possible for two of a vector’s direction angles to be less than 45°
f. What is the value of
2 2 2 sin sin sin
Why
6. Explain the meanings of the terms linearly dependent and coplanar. Make sure you demonstrate
that you understand the difference between the terms, and the situation in which linear
dependency implies coplanarity.
7. Determine if the vectors [1, 3, 4], [4, 2, 2] and [3, 2, 3] are coplanar.
8. Give examples of sets of three vectors that are
a. Collinear
b. Coplanar
c. Not coplanar
GO TO: THE DROPBOX AND UPLOAD YOUR WORK.
9. Explain how you would prove if four given points are coplanar. Use your method to determine if
A (3, 1, 4), B (7, 2, 9), C (0, 8, 2) and D (8, 2, 12) are coplanar.
10. Determine if the following vectors are coplanar. Assume that
1
v ,
2
v
and
3
v
are not coplanar.
a.
1 1 2 w v v 2 7
b.
2 2 3 w v v 2
c.
3 1 3 w v v – 7
Our Service Charter

Excellent Quality / 100% PlagiarismFree
We employ a number of measures to ensure top quality essays. The papers go through a system of quality control prior to delivery. We run plagiarism checks on each paper to ensure that they will be 100% plagiarismfree. So, only clean copies hit customers’ emails. We also never resell the papers completed by our writers. So, once it is checked using a plagiarism checker, the paper will be unique. Speaking of the academic writing standards, we will stick to the assignment brief given by the customer and assign the perfect writer. By saying “the perfect writer” we mean the one having an academic degree in the customer’s study field and positive feedback from other customers. 
Free Revisions
We keep the quality bar of all papers high. But in case you need some extra brilliance to the paper, here’s what to do. First of all, you can choose a top writer. It means that we will assign an expert with a degree in your subject. And secondly, you can rely on our editing services. Our editors will revise your papers, checking whether or not they comply with high standards of academic writing. In addition, editing entails adjusting content if it’s off the topic, adding more sources, refining the language style, and making sure the referencing style is followed. 
Confidentiality / 100% No Disclosure
We make sure that clients’ personal data remains confidential and is not exploited for any purposes beyond those related to our services. We only ask you to provide us with the information that is required to produce the paper according to your writing needs. Please note that the payment info is protected as well. Feel free to refer to the support team for more information about our payment methods. The fact that you used our service is kept secret due to the advanced security standards. So, you can be sure that no one will find out that you got a paper from our writing service. 
Money Back Guarantee
If the writer doesn’t address all the questions on your assignment brief or the delivered paper appears to be off the topic, you can ask for a refund. Or, if it is applicable, you can opt in for free revision within 1430 days, depending on your paper’s length. The revision or refund request should be sent within 14 days after delivery. The customer gets 100% moneyback in case they haven't downloaded the paper. All approved refunds will be returned to the customer’s credit card or Bonus Balance in a form of store credit. Take a note that we will send an extra compensation if the customers goes with a store credit. 
24/7 Customer Support
We have a support team working 24/7 ready to give your issue concerning the order their immediate attention. If you have any questions about the ordering process, communication with the writer, payment options, feel free to join live chat. Be sure to get a fast response. They can also give you the exact price quote, taking into account the timing, desired academic level of the paper, and the number of pages.