Unit 3: Geometry and Trigonometry

Topic 3.12: Vectors (HL only) Questions

Practice 20 exam-style questions for IB Math AA SL Topic 3.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.

1Write down1 mark
2026
Write down the position vector of .
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21 mark
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|(6, 0, 0)ᵀ| equals:
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31 mark
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The vector (0, −7)ᵀ in i, j form is:
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4Write1 mark
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Write the vector −2i + 5j − k in column form.
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51 mark
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Which of these is a unit vector?
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61 mark
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If |v| = 0, then the vector v is:
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7Find2 marks
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Find the unit vector in the direction of a = (6, 8)ᵀ.
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81 mark
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The distance between A and B is found from:
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91 mark
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The position vector of the point (−4, 7) is:
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101 mark
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AB = OB − OA. Then BA equals:
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11Find2 marks
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Find the exact magnitude of v = (1, −2, 2)ᵀ.
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12Show that1 mark
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Show that .
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13Show that1 mark
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Show that .
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14Find2 marks
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Find the magnitude of the vector a = 5i + 12j.
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15Find2 marks
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Points A and B have position vectors OA = (−1, 3)ᵀ and OB = (4, −2)ᵀ. Find AB.
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16Find4 marks
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Find and the unit vector in the direction of .
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17Find3 marks
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Find the vector of magnitude 21 in the direction of d = (6, −2, 3)ᵀ.
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181 mark
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Squaring a component before adding (in the magnitude formula) ensures the result is:
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19Find2 marks
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Find the unit vector in the direction of v = (1, −2, 2)ᵀ.
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20Find3 marks
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The vector (8, p)ᵀ has magnitude 10. Find the possible values of p.
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