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1. The diagram shows two vectors a and b.

Vectors. 1. The diagram shows two vectors a and b. On the grid above draw the vector. 2. Write down as a column vector. (i). (ii). R. The diagram is a sketch. P is the point (2, 3) Q is the point (6, 6). 3. S. Q. a) Write down the vector. Write your answer as a column vector. P.

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1. The diagram shows two vectors a and b.

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  1. Vectors 1.The diagram shows two vectors a and b. On the grid above draw the vector

  2. 2. Write down as a column vector (i) (ii) R The diagram is a sketch. P is the point (2, 3)Q is the point (6, 6) 3. S Q a) Write down the vector Write your answer as a column vector P R is above Q Diagram NOT accurately drawn PQRS is a parallelogram. (b) Find the vector Write your answer as a column vector

  3. 4. PQRS is a trapezium.QP is parallel to RS. R S QP = 3RS Express in terms of a and/or c P Q (i) (ii) Diagrams NOT accurately drawn A 5. OAB is a triangle. P is the point on AB such that AP : PB = 2 : 1 Write in terms of a and b P O B

  4. 6. OPQ is a triangle. Q T is the point on PQ for which PT : TQ = 2 : 1 T (a) Write down, in terms of a and b, an expression for O P (b) Express in terms of a and b. Give your answer in its simplest form. Diagrams NOT accurately drawn X B 7. OABC is a trapezium.OC is parallel to AB. A AB = 2OC X is the point on AB such that AX:XB = 3:1. Express in terms of a and c. O C

  5. 8. OABC is a parallelogram. P is the point on AC such that AP = AC A B (a) Find the vector Give your answer in terms of a and c M P O C The midpoint of CB is M. (b) Prove that OPM is a straight line. As parallelogram, and OPM is a straight line.

  6. C 9. CDEF is a quadrilateral with D M (a) Express in terms of a and b. X (b) Prove that FE is parallel to CD. E F so parallel Diagram NOTaccurately drawn M is the midpoint of DE. (c) Express in terms of a and b. X is the point on FM such that FX : XM = 4 : 1 (d) Prove that C, X and E lie on the same straight line. and CXE is a straight line.

  7. 10.The diagram shows a regular hexagon ABCDEF with centre O. A B Y (a) Express in terms of a and/or b X (i) F C O (ii) X is the midpoint of BC. D E (b) Express in terms of a and/or b Y is the point on AB extended, such that AB : BY = 3:2 (c) Prove that E, X and Y lie on the same straight line and EXY is a straight line. A regular hexagon can be split into 6 equilateral triangles

  8. Proving that the midpoints of any quadrilateral form a parallelogram using vectors C F G a B D b E H c A Therefore 2 pairs of opposite sides with the same length and direction - a parallelogram!

  9. Vectors 1.The diagram shows two vectors a and b. On the grid above draw the vector

  10. 2. Write down as a column vector (i) (ii) The diagram is a sketch. P is the point (2, 3)Q is the point (6, 6) 3. Q a) Write down the vector Write your answer as a column vector P Diagram NOT accurately drawn PQRS is a parallelogram. (b) Find the vector Write your answer as a column vector

  11. 4. PQRS is a trapezium.QP is parallel to RS. R S QP = 3RS Express in terms of a and/or c P Q (i) (ii) Diagrams NOT accurately drawn A 5. OAB is a triangle. P is the point on AB such that AP : PB = 2 : 1 Write in terms of a and b P O B

  12. 6. OPQ is a triangle. Q T is the point on PQ for which PT : TQ = 2 : 1 T (a) Write down, in terms of a and b, an expression for O P (b) Express in terms of a and b. Give your answer in its simplest form. Diagrams NOT accurately drawn X B 7. OABC is a trapezium.OC is parallel to AB. A AB = 2OC X is the point on AB such that AX:XB = 3:1. Express in terms of a and c. O C

  13. 8. OABC is a parallelogram. P is the point on AC such that AP = AC A B (a) Find the vector Give your answer in terms of a and c P O C The midpoint of CB is M. (b) Prove that OPM is a straight line.

  14. C 9. CDEF is a quadrilateral with D M (a) Express in terms of a and b. X (b) Prove that FE is parallel to CD. E F Diagram NOTaccurately drawn M is the midpoint of DE. (c) Express in terms of a and b. X is the point on FM such that FX : XM = 4 : 1 (d) Prove that C, X and E lie on the same straight line.

  15. 10.The diagram shows a regular hexagon ABCDEF with centre O. A B (a) Express in terms of a and/or b X (i) F C O (ii) X is the midpoint of BC. D E (b) Express in terms of a and/or b Y is the point on AB extended, such that AB : BY = 3:2 (c) Prove that E, X and Y lie on the same straight line

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