Lesson F5-F6

F5-F6 Vector product and intersection of lines Quiz: AQA Further Maths, Unit 2

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson F5-F6, Vector product and intersection of lines: 20 multiple choice questions for the AQA Further Maths (7367), Unit 2: Compulsory content, written with Revision Ninja.

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The 20 questions

  1. For non-zero vectors a and b, which expression gives the magnitude of a x b?

    • |a| + |b| sin(theta)
    • |a| |b| sin(theta)
    • |a| |b| tan(theta)
    • |a| |b| cos(theta)

  2. What is the vector product i x j, where i = (1, 0, 0) and j = (0, 1, 0)?

    • (0, 0, 1)
    • (1, 1, 0)
    • (0, 0, -1)
    • 0

  3. Which property of the vector product is true for vectors a, b and c?

    • a x b = b x a
    • a x (b + c) = a x b + a x c
    • a x b is a scalar
    • a x (b x c) = (a x b) x c

  4. What does the equation (r - a) x b = 0 describe for position vector r, with a and b fixed and b non-zero?

    • The point a only
    • The line through a parallel to b
    • The line through a perpendicular to b
    • The plane through a with normal b

  5. Two vectors a and b share a common vertex of a triangle. Which expression gives the area of the triangle?

    • |a x b|
    • (1/2)|a x b|
    • (1/2)|a . b|
    • |a| |b|

  6. What is the perpendicular distance from a point P to the line r = a + lambda b?

    • |p - a| |b|
    • |(p - a) x b| / |b|
    • |(p - a) . b| / |b|
    • |(p - a) x b| |b|

  7. What is the perpendicular distance from the point (x0, y0, z0) to the plane ax + by + cz = d?

    • |a x0 + b y0 + c z0 - d| / sqrt(a^2 + b^2 + c^2)
    • |a x0 + b y0 + c z0 - d| / (a^2 + b^2 + c^2)
    • |a x0 + b y0 + c z0| / sqrt(a + b + c)
    • a x0 + b y0 + c z0 - d

  8. Find the area of the triangle with vertices A(1, 0, 0), B(0, 2, 0) and C(0, 0, 3).

    • 49/2
    • 7
    • sqrt(7)
    • 7/2

  9. Find the vector product (1, 2, 3) x (4, 5, 6).

    • (-3, 6, -3)
    • (3, -6, 3)
    • (-3, 6, 3)
    • (-3, -6, -3)

  10. What is the area of the equilateral triangle with vertices (1, 0, 0), (0, 1, 0) and (0, 0, 1)?

    • 3/2
    • sqrt(2)/2
    • sqrt(3)/2
    • 1/2

  11. What is the magnitude of the vector product of a = (1, 2, 0) and b = (2, -1, 0)?

    • 5
    • 0
    • sqrt(5)
    • 3

  12. Which vector is perpendicular to both (1, 1, 0) and (0, 1, 1)?

    • (1, -1, -1)
    • (1, 1, 1)
    • (1, -1, 1)
    • (2, 0, 0)

  13. Find the point where the lines r = (1, 0, 0) + s(1, 1, 0) and r = (0, 2, 0) + t(1, -1, 0) intersect.

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

  14. Find the perpendicular distance from the point (1, 2, 3) to the plane x - 2y + 2z = 9.

    • 2/3
    • 1/2
    • 2
    • 6

  15. Find the point where the line r = (1, 2, 3) + t(1, 1, 1) meets the plane x + y + z = 12.

    • (3, 4, 5)
    • (2, 3, 4)
    • (3, 4, 6)
    • (4, 5, 6)

  16. What is the perpendicular distance from the point (0, 3, 4) to the line through the origin with direction (1, 0, 0)?

    • 5
    • 7
    • 4
    • 3

  17. Are the lines r = (1, 0, 0) + s(1, 1, 1) and r = (0, 1, 0) + t(1, 0, 1) skew, intersecting or parallel?

    • Skew: not parallel and they do not intersect
    • They intersect at (2, 1, 1)
    • They are parallel
    • They intersect at (1, 1, 0)

  18. Two skew lines are r = (1, 0, 0) + s(0, 1, 0) and r = (0, 0, 1) + t(1, 0, 0). What is the perpendicular distance between them?

    • 2
    • 1
    • sqrt(2)
    • 0

  19. A parallelogram has adjacent sides (1, 0, 2) and (0, 3, 1). What is its area?

    • sqrt(46)
    • sqrt(38)
    • sqrt(46)/2
    • 46

  20. Find the point where the line x = 1 + t, y = 2 - t, z = 3 + 2t meets the plane x - y + z = 1.

    • (1, 2, 3)
    • (3/4, 9/4, 5/2)
    • (3/4, 7/4, 5/2)
    • (0, 3, 1)

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