Unit 3: Geometry and Trigonometry
Topic 3.13: Scalar product (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.13. 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 scalar (dot) product of two vectors is:
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If v·w = 0 and neither vector is zero, the angle between them is:
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i·i (where i is the unit vector (1,0,0)) equals:
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Vectors are a = (2, 3, −1) and b = (4, −1, 5). Find a·b.
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Write down a vector parallel to that is twice as long.
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Two non-zero vectors are parallel exactly when:
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Two non-zero vectors are perpendicular exactly when:
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If a·b is negative, the angle between a and b is:
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For u = (3,4) and v = (4,−3), the angle between them is:
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Vectors a = (5, −2, 1) and b = (2, k, −3) are perpendicular. Find the value of k.
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Vectors (a, 6) and (2, −4) are parallel. The value of a is:
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Vectors are p = (k, 2, −1) and q = (3, k, 1). Given that p·q = 7, find the value of k.
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Find the angle, to the nearest degree, between a = (4, 3) and b = (−1, 2).
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Vectors u = (6, −4, 8) and v = (3, m, 4) are parallel. Find the value of m.
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Find the angle between u = (1, 0, 1) and v = (0, 1, 1), giving your answer in degrees.
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Find a vector that is perpendicular to (2, −5) and has magnitude 1.
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