Exercise 1 (Basic Addition/Subtraction) Again and . is a point such that What is: Write each vector in terms of and/or . is a regular hexagon with centre . and . a. c. d. Express in terms of and/or : is a parallelogram. is a point such that . is a. b. c. d. a point such that . Determine: a. b. c. d. a. b. c. d. Exercise 2 (Using Ratios) Write each vector in terms of and/or . In the diagram, is the midpoint of , , , and a. b. c. d. and . Express these vectors in terms of , In the following diagram and . is a point Write each vector in terms of and/or . and . such that a. b. c. d. What is: e. f. a. b. c. d. a. b. c. d. e. In the following diagram, is a point such that . is a parallelogram. is the point on such that . a. b. c. Find the vector . Give your answer in terms of and . Exercise 3 (Finding More Complex Paths) Exercise 4 (Proof Questions) Given that the midpoint of is , is a parallelogram. is the midpoint of . is prove that is a straight line. , and a point such that . Determine: and and and . is the midpoint of . Prove Express in terms of and . a. b. c. d. e. f. g. that is a straight line. Prove that is parallel to . is the midpoint of . is the midpoint of . Express in terms of and . Determine the vectors: is the point on such that such a. b. c. d. that . Prove that , and lie on the Mark points on the diagram such that , same straight line. and . Hence find: OLD ANSWERS (DO NOT PRINT) Exercise 1
Exercise 1 (Basic Addition/Subtraction) Write each vector in terms of and/or . a. b. c. d. Write each vector in terms of and/or . a. b. c. d. Write each vector in terms of and/or . is a regular hexagon with centre . and . Express in terms of and/or : a. b. c. d. Exercise 2 (Using Ratios) In the following diagram and . is a point such that What is: a. b. c. d. Again and . is a point such that What is: a. c. d. is a parallelogram. is a point such that . is a point such that . Determine: a. b. c. d. In the diagram, is the midpoint of , , , and and . Express these vectors in terms of , and . a. b. c. d. e. f. Exercise 3 (Finding More Complex Paths) is a parallelogram. is the midpoint of . is a point such that . Determine: a. b. c. d. e. f. g. is the midpoint of . Determine the vectors: a. b. c. d. Mark points on the diagram such that , and . Hence find: a. b. c. d. e. In the following diagram, is a point such that . a. b. c. Exercise 4 (Proof Questions) , and Express in terms of and . Prove that is parallel to . is the midpoint of . Express in terms of and . is the point on such that such that . Prove that , and lie on the same straight line. is a parallelogram. is the point on such that . Find the vector . Give your answer in terms of and . Given that the midpoint of is , prove that is a straight line. and and and . is the midpoint of . Prove that is a straight line. OLD ANSWERS (DO NOT PRINT) Exercise 1
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