1. If a and b denote the vectors OA and OB, indicate on the same diagram...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. If a and b denote the vectors OA and OB, indicate on the same diagram the vectors OC and OD denoted by a+b and a- b. Draw on another diagram the vector OE denoted by a +2b. 2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (ii) BD and (iv) AC. 3. OABC is a tetrahedron and OA = a, OB = b and OC = c. The points P and Q are such that OA = AP and 20B = BQ. The point M is the midpoint of PQ. Find (i) AB, (ii) PQ, (ii) CQ, (iv) QM, (v) MB and (vi) OM in terms of a, b and c. 4. ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x and y. What can you deduce about the directed line-segments BC and PQ? 5. ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. 7. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD, (iv) AC. 8. ABC is a triangle and P is any point in BC. If PQ is the resultant of AP, PB, PC, show that ABQC is a parallelogram, and Q is therefore a fixed point. 1. If a and b denote the vectors OA and OB, indicate on the same diagram the vectors OC and OD denoted by a+b and a- b. Draw on another diagram the vector OE denoted by a +2b. 2. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (ii) BD and (iv) AC. 3. OABC is a tetrahedron and OA = a, OB = b and OC = c. The points P and Q are such that OA = AP and 20B = BQ. The point M is the midpoint of PQ. Find (i) AB, (ii) PQ, (ii) CQ, (iv) QM, (v) MB and (vi) OM in terms of a, b and c. 4. ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x and y. What can you deduce about the directed line-segments BC and PQ? 5. ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. 6. ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC. 7. ABCD is a square and P, Q are the midpoints of BC, CD respectively. If AP = a and AQ = b, find in terms of a and b, the directed line segments (i) AB, (ii) AD, (iii) BD, (iv) AC. 8. ABC is a triangle and P is any point in BC. If PQ is the resultant of AP, PB, PC, show that ABQC is a parallelogram, and Q is therefore a fixed point.
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
I need it in a few minutes please Answer all questions Given: Wednesday 1 July, 2020, 9:00 a.m. Due: Wednesday 1 July, 2020, 3:00 p.m. 1) [6 marks] A function g is defined by a+1| if r# -1, g(x) = 1...
-
Explain manifesto to vying for the main compound perfect in Notre Dame girls SHS indicating major points for winning that position?
-
Please I need it in 20mins time please Q 3. A company manufactures and sells a smartphones per month. The monthly cost and price demand equations are C(x) = 72, 000 + 60r p = 200 30 0S2 < 6000 (a)...
-
The following inventory information is available for Ricci Manufacturing Corporation for the year ended December 31, 2017: Beginning Ending Inventories: Raw materials Work in process Finished goods...
-
Wendy Jones of Whitehorse has hired you as her bookkeeper to record the following transactions in the cash payments journal. She would like you to record and post as appropriate and supply her with a...
-
Switch S has been closed for a long time, and the electric circuit shown in Figure P28.68 carries a constant current. Take C1 = 3.00 μF, C2 = 6.00 μF, R1 = 4.00 kΩ, and R2 = 7.00...
-
Robert Carr is the founder of Heartland Payment Systems, Inc. Carr was heavily involved in negotiations with Global Payments, Inc., concerning the acquisition of Heartland by Global. During this...
-
Decorative Steel, Inc., began August with 55 units of iron inventory that cost $35 each. During August, the company completed the following inventory transactions: Requirements 1. Prepare a perpetual...
-
Pick one of the different types of SQL statements (data definition language, data manipulation language, or data control language). Explain how that type of statement is used, and how you would use...
-
Jocame Inc. began business on January 2, 20Y7. Salaries were paid to employees on the last day of each month, and social security tax, Medicare tax, and federal income tax were withheld in the...
-
Determine the points at which the function fhas discontinuities. Use the continuity checklist to give a reason for each point of discontinuity. Use the continuity checklist to determine if the...
-
Explain how the criminal law could provide a backup for the tort law to hold someone accountable, how the tort law could back up the criminal law to provide some degree of accountability, and how...
-
Explain: transition materials concluding materials supporting materials introductory materials. give example also.
-
provide the output of the following program after execution. Display the output properly in the box to your right. #include #include using namespace std; int main() { int a=2,b,c; double r=22.0,...
-
On a map where each unit represents one kilometer, two marinas are located at P(4,2) and Q(8,12). If a boat travels in a straight line from one marina to the other, how far does the boat travel?
-
List three (3) examples of the tools and equipment that are used for partial highlighting and foiling.
-
What are the conditions needed for constructive interference? What are the conditions needed for destructive interference? How do these relate to acoustic resonance?
-
An Atomic Energy Commission nuclear facility was established in Hanford, Washington, in 1943. Over the years, a significant amount of strontium 90 and cesium 137 leaked into the Columbia River. In a...
-
A student goes to breakfast one out of every two class days (50% of the time). What is the probability that, in the next five class days, this student will go to breakfast? a. Exactly three days b....
-
Joe stands 67.00 in. tall. What percentage of American men are (a) the same height or shorter than Joe, (b) taller than Joe, and (c) between the mean and Joes' height?
-
Assume a frequency curve for the following sets of data. What shape will the curve probably take? Use the following key: NO = normal NS = negatively skewed PS = positively skewed BI = bimodal RE =...
-
10.A company contracted with a marketing firm to construct software and create a business website. A quote was requested and accepted. Sometime later, the business asked for updates and revisions but...
-
George Oppenheimer, an agent for Wellington Farms of Massachusetts, Inc., had contacted Mark Kiriakou from the Capital Area Food Bank regarding an order for frozen turkey meat. In an exchange of...
-
Extreme Machine manufactures machines and parts for various industries; they have an office in Youngstown, Ohio. Avery Dennison manufactures and sells labels from a plant in Mentor, Ohio. They use...
Study smarter with the SolutionInn App