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MCV 4U

Unit 3 Assignment

1. Indicate whether the following are scalars or vectors. [5K marks]

a) 40 km/h downward __________

b) 10 km __________

c) downward force of 12 N__________

d) distance of the moon from Earth__________

e) 100 km/h on a bearing of 230。__________

2. List as many equal vectors as possible for each diagram. [2A marks]

3. Draw to scale (use a ruler) using the vectors and below. [2A+1C marks]

4. ABCD is a rectangle where and , where . Draw a diagram that includes the two vectors and , that are both drawn inside the rectangle ABCD [2A+1C marks]

5. If = [–1,–1], = [2, 6], and = [–11, –8], express as a linear combination of and .[2T marks]

6. A boat on a lake is heading at a bearing of 40º. The boat is traveling at a velocity of 40 km/h and the current is flowing from the southeast at 9 km/h. Determine the heading of the boat and the resultant velocity relative to the ground. [2A2T1C marks]

7. PQRS is a parallelogram shown below. Points T and W are the midpoints of PS and QR, respectively. If , and express the following vectors as linear combinations of and with justification for question b [2A +2A+2T+2C marks]

a)

b)

8. An aircraft on a bearing of 170º and travelling at 200 km/h is affected by a wind bearing 270º and blowing at 75 km/h. Find the Equilibrant vector (USING Vector decomposition method) in scalar component form [2A2T1C marks]

9. If and , determine if the following vector pairs are paralle. [2K2A marks]

10. Given the points A(-1,2) and B(2,5), determine: [1K1A marks]

11. Given = (2,0, −1) and = (0,−2,3) , determine the following: [1K1A marks]

12. Calculate the following using these vectors: where “e” is your birth-month , Show all your steps for full marks