Unit 3: Geometry and Trigonometry
Topic 3.16: Vector product (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.16. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
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The parallelogram with sides v and w has area:
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For i×j (axis unit vectors), the result is:
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Given v = (3, −1, 2) and w = (0, 4, 1), find v×w.
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Points A(1, 0, 2), B(3, 1, 2) and C(2, −1, 4). Find AB×AC.
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If v×w = 0 (the zero vector) for non-zero v, w, then v and w are:
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Find a vector perpendicular to both a = (1, 1, 0) and b = (0, 1, 1).
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|v×w| is largest (for fixed magnitudes) when the angle between v and w is:
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Vectors a and b have |a| = 7, |b| = 2 and the angle between them is 60°. Find |a×b|.
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Find the area of the parallelogram with adjacent sides v = (1, 2, 2) and w = (3, 0, −1).
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Vectors p = (1, −2, 2) and q = (3, 0, 1). (a) Find p×q. (b) Hence find q×p.
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Points A(0, 0, 0), B(2, 1, 2) and C(t, 0, 0) lie in space. (a) Find AB×AC in terms of t. (b) Find the value of t > 0 that makes the area of triangle ABC equal to 3.
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