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Express vector paths in terms of a and b

10th grade (Year 11 in England) · 16 questions · Common Core: HSN.VM.B.4 · England: GCSE Higher Geometry

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  1. Question 1

    OA = a and OB = b. P lies on AB with AP : PB = 1 : 3. Find OP in terms of a and b.

    • A. (3/4)a + (1/4)b
    • B. (1/4)a + (3/4)b
    • C. (1/4)b − (1/4)a
    • D. (1/2)a + (1/2)b

  2. Question 2

    OA = a and OB = b. M is the midpoint of AB. Find AB in terms of a and b.

    • A. b − a
    • B. 2b − a
    • C. a + b
    • D. a − b

  3. Question 3

    OA = a and OB = b. P lies on AB with AP : PB = 2 : 1. Find OP in terms of a and b.

    • A. (2/3)b − (2/3)a
    • B. (2/3)a + (1/3)b
    • C. (1/3)a + (2/3)b
    • D. (1/2)a + (1/2)b

  4. Question 4

    OA = a and OB = b. M is the midpoint of AB. Find AB in terms of a and b.

    • A. a − b
    • B. b − a
    • C. 2b − a
    • D. a + b

  5. Question 5

    OA = a and OB = b. P lies on AB with AP : PB = 1 : 3. Find OP in terms of a and b.

    • A. (1/4)a + (3/4)b
    • B. a + (1/4)b
    • C. (3/4)a + (1/4)b
    • D. (1/4)b − (1/4)a

  6. Question 6

    OA = a and OB = b. M is the midpoint of AB. Find AM in terms of a and b.

    • A. ½b − ½a
    • B. a − b
    • C. ½a − ½b
    • D. ½a + ½b

  7. Question 7

    OA = a and OB = b. P lies on AB with AP : PB = 1 : 3. Find OP in terms of a and b.

    • A. (1/2)a + (1/2)b
    • B. (1/4)a + (3/4)b
    • C. (3/4)a + (1/4)b
    • D. a + (1/4)b

  8. Question 8

    OA = a and OB = b. M is the midpoint of AB. Find MB in terms of a and b.

    • A. ½b − ½a
    • B. a + b
    • C. ½a + ½b
    • D. ½a − ½b

  9. Question 9

    OA = a and OB = b. P lies on AB with AP : PB = 3 : 1. Find OP in terms of a and b.

    • A. (1/2)a + (1/2)b
    • B. (3/4)b − (3/4)a
    • C. (1/4)a + (3/4)b
    • D. a + (3/4)b

  10. Question 10

    OA = a and OB = b. M is the midpoint of AB. Find BA in terms of a and b.

    • A. a − b
    • B. ½a − ½b
    • C. ½a + ½b
    • D. ½b − ½a

  11. Question 11

    OA = a and OB = b. P lies on AB with AP : PB = 3 : 1. Find OP in terms of a and b.

    • A. (3/4)a + (1/4)b
    • B. (1/2)a + (1/2)b
    • C. a + (3/4)b
    • D. (1/4)a + (3/4)b

  12. Question 12

    OA = a and OB = b. M is the midpoint of AB. Find MB in terms of a and b.

    • A. a − b
    • B. ½b − ½a
    • C. a + b
    • D. ½a + ½b

  13. Question 13

    OA = a and OB = b. P lies on AB with AP : PB = 1 : 2. Find OP in terms of a and b.

    • A. (1/2)a + (1/2)b
    • B. (1/3)a + (2/3)b
    • C. (1/3)b − (1/3)a
    • D. (2/3)a + (1/3)b

  14. Question 14

    OA = a and OB = b. M is the midpoint of AB. Find BA in terms of a and b.

    • A. ½b − ½a
    • B. a − b
    • C. 2b − a
    • D. a + b

  15. Question 15

    OA = a and OB = b. P lies on AB with AP : PB = 3 : 1. Find OP in terms of a and b.

    • A. a + (3/4)b
    • B. (3/4)a + (1/4)b
    • C. (3/4)b − (3/4)a
    • D. (1/4)a + (3/4)b

  16. Question 16

    OA = a and OB = b. M is the midpoint of AB. Find BA in terms of a and b.

    • A. ½a + ½b
    • B. a − b
    • C. a + b
    • D. b − a

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  1. (3/4)a + (1/4)b
  2. b − a
  3. (1/3)a + (2/3)b
  4. b − a
  5. (3/4)a + (1/4)b
  6. ½b − ½a
  7. (3/4)a + (1/4)b
  8. ½b − ½a
  9. (1/4)a + (3/4)b
  10. a − b
  11. (1/4)a + (3/4)b
  12. ½b − ½a
  13. (2/3)a + (1/3)b
  14. a − b
  15. (1/4)a + (3/4)b
  16. a − b