Lesson J3-J4

J3-J4 Vector operations and position vectors Quiz: AQA Maths, Unit 10

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

In partnership with Revision Ninja

Lesson J3-J4, Vector operations and position vectors: 20 multiple choice questions for the AQA Maths (7357), Unit 10: Vectors, written with Revision Ninja.

Host it live on the board and students join with a game code on their own devices, or revise alone with Free Play. The answers are revealed in the game.

Host this setFree Play

The 20 questions

  1. What does the position vector OP of a point P(x, y) equal?

    • (x, y), the vector from P to O
    • A vector of length 1
    • A unit vector along the x-axis
    • (x, y), the vector from the origin O to P

  2. If points A and B have position vectors a and b, what is the vector AB?

    • b - a
    • (a + b)/2
    • a + b
    • a - b

  3. What is the effect of multiplying a vector v by a scalar k?

    • It adds k to each component
    • It multiplies the magnitude by |k|, and reverses the direction when k is negative
    • It always doubles the magnitude
    • It leaves the magnitude unchanged

  4. In the triangle law of vector addition, what does a + b represent when a and b are placed head to tail?

    • The difference of a and b
    • The product of the magnitudes of a and b
    • The single vector from the tail of a to the head of b
    • The vector from the head of a to the head of b

  5. If A and B have position vectors a and b, what is the position vector of the midpoint of AB?

    • (b - a)/2
    • (a + b)/2
    • a + b
    • b - a

  6. For a = (2, 3) and b = (5, -1), what is a + b?

    • (7, 2)
    • (3, -4)
    • (7, 4)
    • (10, -3)

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

    • (-1, 10)
    • (-1, 6)
    • (1, 10)
    • (5, 6)

  8. Points P(-2, 1) and Q(4, 9) are given. What is the distance PQ?

    • 10
    • sqrt(52)
    • 14
    • 7

  9. What is the midpoint of the points A(-2, 1) and B(4, 9)?

    • (1, 4)
    • (2, 5)
    • (3, 8)
    • (1, 5)

  10. Points A and B have position vectors (0, 0) and (6, 9). P lies on AB with AP:PB = 1:2. What is the position vector of P?

    • (2, 3)
    • (1, 1.5)
    • (4, 6)
    • (3, 4.5)

  11. If a = (3, -4), what is the magnitude of 2a?

    • 5
    • 14
    • 10
    • 20

  12. What is the unit vector parallel to (5, 12)?

    • (1/5, 12/5)
    • (5/12, 1)
    • (5/13, 12/13)
    • (13/5, 12/5)

  13. Vectors (2, k) and (6, 9) are parallel. What is k?

    • 3
    • 9
    • 1/3
    • 6

  14. Points A(1, 2), B(3, 6) and C(5, 10) are given. Which statement is true?

    • A, B and C form a right angle at B
    • A, B and C are collinear because AB = BC
    • A, B and C form a triangle of area 2
    • AB is perpendicular to BC

  15. If AB = b - a, what is BA?

    • a + b
    • b - a
    • a - b
    • -(a + b)

  16. Vectors a = (1, 2) and b = (4, -2) are given. What is c = 2a - b?

    • (6, -2)
    • (-2, 6)
    • (-2, 2)
    • (2, 6)

  17. What positive value of k makes |k(3, 4)| equal to 10?

    • 1/2
    • 5
    • 2
    • 10

  18. Points P(2, -1) and Q(5, 3) are given. Point R satisfies PR = 2PQ. What are the coordinates of R?

    • (8, 7)
    • (6, 8)
    • (4, -2)
    • (11, 11)

  19. Vectors a = 2i + 3j and b = i - j are given. What is 3a - 2b?

    • 8i + 7j
    • 4i + 7j
    • 8i + 11j
    • 4i + 11j

  20. A line passes through points with position vectors a and b. Which vector equation gives the points on the line?

    • r = a + t(b - a), for real t
    • r = (a + b)t
    • r = a - t(a + b)
    • r = a + tb, for 0 <= t <= 1

All AQA Maths quizzes