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CAIE A Level Mathematics 9709

Vectors questions

Exam-style questions on Vectors, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationPoint A has position vector (0, 0, 0) and point B has position vector (1, 2, 2). Find the magnitude of vector AB.
  2. 2 marksFoundationGiven the vectors a = -4i + 3j - 2k and b = 3i - 4j - 2k, compute the scalar product a · b.
  3. 2 marksFoundationFind the scalar product of the vectors a = 2i - 1j - 2k and b = -1i - 2j - 2k.
  4. 3 marksFoundationTwo vectors are a = 5i - 4j + 4k and b = -5i + 4j + 5k.
  5. 3 marksStandardThe vectors p = 5i - j + 2k and q = 3i + 5j + lambdak are perpendicular.
  6. 3 marksStandardThe vector v = 12i + lambdaj + 4k has magnitude 14, and λ is positive.
  7. 3 marksChallengePoints A and B have position vectors overrightarrowOA = 6i - 3j and overrightarrowOB = 10i - 3j. The point P lies on AB so that AP : PB = 1 : 3.