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# Vectors

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Need help with vectors? then here are some questions to help

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### Vectors

2. 2. Leave blank 1. OPT is a triangle. M is the midpoint of OP. OT = a TP = b (a) Express OM in terms of a and b. OM =........................... (2) (b) Express TM in terms of a and b. Give your answer in its simplest form. TM = ........................... (2) Q1 (Total 4 marks) Diagram NOT accurately drawn M P O Ta b Lots more free past papers at http://bland.in
3. 3. Leave blank 2. OAB is a triangle. OA = a OB = b (a) Find the vector AB in terms of a and b. AB = ........................................ (1) P is the point on AB such that AP : PB = 3 : 2 (b) Show that OP = 1 5 (2a + 3b) (3) Q2 (Total 4 marks) A a O Diagram NOT accurately drawn P B b Lots more free past papers at http://bland.in
4. 4. Leave blank 3. OAB is a triangle. OA = a, OB = b (a) Find the vector AB in terms of a and b. AB = ............................ (1) P is the point on AB so that AP : PB = 2 : 1 (b) Find the vector OP in terms of a and b. Give your answer in its simplest form. OP = ............................ (3) Q3 (Total 4 marks) A Diagram NOT accurately drawna P O B b Lots more free past papers at http://bland.in
5. 5. Leave blank 4. OABC is a parallelogram. M is the midpoint of CB. N is the midpoint of AB. (a) Find, in terms of a and/or c, the vectors (i) ....................................................... (ii) ....................................................... (2) (b) Show that CA is parallel to MN. (2) Q4 (Total 4 marks) Diagram NOT accurately drawn O BN Cc a M A OA OC = = a c MB , MN . Lots more free past papers at http://bland.in
6. 6. Leave blank 5. = 2a + bOX = 4a + 3bOY (a) Express the vector XY in terms of a and b Give your answer in its simplest form. ..................................... (2) Y 4a + 3b O 2a + b X Diagram NOT accurately drawn Lots more free past papers at http://bland.in
7. 7. Leave blank XYZ is a straight line. XY : YZ = 2 : 3 (b) Express the vector OZ in terms of a and b Give your answer in its simplest form. ..................................... (3) Q5 (Total 5 marks) Z Y 4a + 3b O 2a + b X Diagram NOT accurately drawn Lots more free past papers at http://bland.in
8. 8. Leave blank 6. Diagram NOT accurately drawn ABCD is a parallelogram. AB is parallel to DC. AD is parallel to BC. AB = p AD = q (a) Express, in terms of p and q (i) AC (i)................................. (ii) BD (ii)................................ (2) Diagram NOT accurately drawn AC and BD are diagonals of parallelogram ABCD. AC and BD intersect at T. (b) Express AT in terms of p and q. ..................................... (1) (Total 3 marks) A p B q D C A p B q T D C Q6 Lots more free past papers at http://bland.in
9. 9. Leave blank 7. OPT is a triangle. M is the midpoint of OP. OT = a TP = b (a) Express OM in terms of a and b. OM =........................... (2) (b) Express TM in terms of a and b. Give your answer in its simplest form. TM = ........................... (2) Q7 (Total 4 marks) Diagram NOT accurately drawn M P O Ta b Lots more free past papers at http://bland.in
10. 10. Leave blank 8. O A B 3b 2a P OAB is a triangle. OA = 2a OB = 3b (a) Find AB in terms of a and b. AB = ............................ (1) P is the point on AB such that AP : PB = 2 : 3 (b) Show that OP is parallel to the vector a + b. (3) Q8 (Total 4 marks) Diagram NOT accurately drawn Lots more free past papers at http://bland.in