QQQ – Vectors Name _______________ On the following diagram, ABCD 3) is a parallelogram, and , and Q is a point such that OABC is a parallelogram. Determine, in terms of a and b: is the point on such that . ______________ (1) . . ______________ (1) Find the vector . Give your answer in terms of and . (2) The midpoint of is . 2. is a triangle. OAB Prove that is a straight line. (3) is the midpoint of X AB. is the midpoint of Y OB. is the point on such that Z OX : = 2 : 1 OZ ZX = 3a, = 3b Score: _____ /14 Award ____________ (a) Find, in terms of a and b, the vectors Answers (i) a) (1 mark) b) (1 mark) ............................ (1) ai) (1 mark) aii) (2 marks) aiii) (2 marks) (ii) b) We have so far found that . So . ............................ (2) (2 marks) a) (2 marks) (iii) b) ............................ (2) is a multiple of , so is parallel (1) (3 (b) and are on a straight A, Z Y marks total) line. Find the ratio : AZ ZY 14 marks: Platinum 12 marks: Gold ............................ 11 marks: Silver (2) 9 marks: Bronze
QQQ – Vectors Name _______________ On the following diagram, ABCD is a parallelogram, and , and Q is a point such that Determine, in terms of a and b: ______________ (1) ______________ (1) 2. OAB is a triangle. X is the midpoint of AB. Y is the midpoint of OB. Z is the point on OX such that OZ : ZX = 2 : 1 = 3a, = 3b (a) Find, in terms of a and b, the vectors (i) ............................ (1) (ii) ............................ (2) (iii) ............................ (2) (b) A, Z and Y are on a straight line. Find the ratio AZ : ZY ............................ (2) 3) OABC is a parallelogram. is the point on such that . . . Find the vector . Give your answer in terms of and . (2) The midpoint of is . Prove that is a straight line. (3) Score: _____ /14 Award ____________ Answers a) (1 mark) b) (1 mark) ai) (1 mark) aii) (2 marks) aiii) (2 marks) b) We have so far found that . So . (2 marks) a) (2 marks) b) is a multiple of , so is parallel (1) (3 marks total) 14 marks: Platinum 12 marks: Gold 11 marks: Silver 9 marks: Bronze
QQQ-Vectors.docx