Lesson 1.10d

1.10d Vector operations Quiz: OCR Maths, Unit 10

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.10d, Vector operations: 20 multiple choice questions for the OCR Maths (H240), Unit 10: Vectors, written with Revision Ninja.

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The 20 questions

  1. How are two vectors arranged diagrammatically to perform vector addition?

    • Head to tail
    • Parallel alignment
    • Head to head
    • Tail to tail

  2. What effect does multiplying a vector by a negative scalar have on its direction?

    • Reverses it
    • Keeps it unchanged
    • Makes it zero
    • Rotates it 90°

  3. What is the magnitude of any unit vector?

    • 2
    • 1
    • Infinity
    • 0

  4. From which point is a position vector measured?

    • The target point
    • The y-axis
    • The x-axis
    • The origin

  5. If a = 2i + 3j, what is -a?

    • 2i - 3j
    • -2i + 3j
    • -3i - 2j
    • -2i - 3j

  6. For two vectors to be equal, what two properties must they share?

    • Magnitude and direction
    • Components and position
    • Magnitude and origin
    • Direction and position

  7. What is the magnitude of the zero vector?

    • Undefined
    • 1
    • 0
    • Infinity

  8. For a = 3i + 2j and b = i - 4j, what is a + b?

    • 2i - 2j
    • 4i + 6j
    • 4i - 2j
    • 2i + 6j

  9. For a = (1, 4) and b = (2, -1), what is 2a - 3b?

    • (4, 11)
    • (-4, 5)
    • (8, -11)
    • (-4, 11)

  10. Position vectors are p = 2i + 3j and q = 5i - j. What is the vector PQ?

    • 3i - 4j
    • 7i + 2j
    • -3i + 4j
    • 3i + 4j

  11. What is the position vector of the midpoint of A(1, 2) and B(5, 6)?

    • 3i + 4j
    • 2i + 2j
    • 6i + 8j
    • 4i + 4j

  12. A is the origin and B is (6, 9). What is the point dividing AB in the ratio 1:2?

    • (3, 4.5)
    • (4, 6)
    • (2, 3)
    • (6, 9)

  13. In triangle ABC, AB = a and BC = b. Which expression gives AC?

    • a - b
    • a + b
    • -a - b
    • b - a

  14. If OP = 3i - 2j, what is 2OP?

    • 5i - 4j
    • 6i + 4j
    • 3i - 4j
    • 6i - 4j

  15. Which vector is parallel to 2i - 6j?

    • i + 3j
    • 3i - j
    • i - 3j
    • 2i + 6j

  16. The vectors a = 2i + 3j and b = 4i + lambda j are parallel. What is lambda?

    • 6
    • 3
    • -6
    • 8

  17. In parallelogram ABCD, AB = a and AD = b. Which expression gives BC?

    • b - a
    • b
    • a + b
    • a

  18. Point R divides PQ with PR : RQ = 3 : 1, where P = (1, 1) and Q = (5, 9). What are the coordinates of R?

    • (3, 5)
    • (2, 3)
    • (4, 7)
    • (4, 8)

  19. Given a = i + 2j and b = 3i - j, what is 2a + b?

    • 5i + 3j
    • 5i + 5j
    • 7i + 3j
    • -i + 5j

  20. Points A = (0, 8) and B = (4, 0) have position vectors OA and OB. If OR = (1 - t)OA + tOB with t = 1/4, what is R?

    • (3, 2)
    • (1, 6)
    • (0, 6)
    • (1, 2)

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