Lesson 1.10g

1.10g Problem solving with vectors in pure mathematics and context Quiz: OCR Maths, Unit 10

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.10g, Problem solving with vectors in pure mathematics and context: 20 multiple choice questions for the OCR Maths (H240), Unit 10: Vectors, written with Revision Ninja.

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The 20 questions

  1. What term describes a quantity that has magnitude but no direction?

    • A scalar
    • A vector
    • A modulus
    • A displacement

  2. How is the magnitude of a 3D vector a written using modulus bars?

    • [a]
    • |a|
    • (a)
    • <a|

  3. What is the magnitude of the 2D vector 3i - 4j?

    • 1
    • 7
    • 25
    • 5

  4. What is the magnitude of the 3D position vector 2i + j + 2k?

    • 9
    • 3
    • 5
    • 4

  5. In 2D, vector direction is usually measured counter-clockwise from which line?

    • Negative x-axis
    • Positive y-axis
    • Positive x-axis
    • Negative y-axis

  6. Which vector is a unit vector in the direction of 6i + 8j?

    • 0.5i + 0.5j
    • 3i + 4j
    • 0.6i + 0.8j
    • 12i + 16j

  7. What is the position vector of point B relative to origin O denoted as?

    • BO
    • BA
    • AB
    • OB

  8. If OA = 2i + 3j and OB = 5i + 7j, what is vector AB?

    • 10i + 21j
    • -3i - 4j
    • 7i + 10j
    • 3i + 4j

  9. A particle moves from (1, 2, 3) to (4, 2, 7). What is its displacement vector?

    • 3i + 10k
    • 3i + 4j + 4k
    • 3i + 4k
    • 5i + 4j + 10k

  10. Two non-zero vectors are parallel if and only if one is what of the other?

    • The dot product
    • The modulus
    • The unit vector
    • A scalar multiple

  11. If a = 2i - j + 3k and b = 4i - 2j + xk are parallel, what is x?

    • 5
    • 6
    • 3
    • -6

  12. What is the distance between points P(1, -2, 4) and Q(3, -2, 1)?

    • 5
    • 13
    • sqrt(13)
    • sqrt(5)

  13. What is a vector with a magnitude of one called?

    • A unit vector
    • A scalar vector
    • A zero vector
    • A position vector

  14. What is vector a of magnitude 10 at angle 60 degrees to the positive x-axis?

    • 10i + 10j
    • 5sqrt(3)i + 5j
    • 5i + 5j
    • 5i + 5sqrt(3)j

  15. If midpoint M of line AB has position vector 3i + 4j and A is i + 2j, what is B?

    • 7i + 10j
    • 2i + 2j
    • 5i + 6j
    • 4i + 6j

  16. What is the vector result of adding displacement AB to displacement BC?

    • CB
    • BA
    • CA
    • AC

  17. A force of (2i + 5j) N and (3i - 2j) N act on an object. What is the resultant force?

    • 5i + 3j N
    • 6i - 10j N
    • 5i + 7j N
    • -i + 7j N

  18. A boat travels with velocity (3i + 4j) m/s for 5 seconds. What distance does it travel?

    • 12 m
    • 7 m
    • 25 m
    • 35 m

  19. What is the angle in degrees between vector i + j and the positive x-axis?

    • 45
    • 30
    • 90
    • 60

  20. In a triangle ABC with position vectors a, b, c, what is the centroid's position vector?

    • a + b + c
    • (a + b + c)/2
    • (a + b + c)/3
    • (a + b + c)/6

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