Unit 3: Geometry and Trigonometry
Topic 3.13: Scalar & vector products (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 3.13. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
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Find a·b where a = (5, −2, 1) and b = (3, 4, −2).
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Find a vector perpendicular to both u = (2, −1, 0) and z = (1, 3, 2).
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To find a vector perpendicular to BOTH u and z, you compute:
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The scalar (dot) product of two vectors is always:
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If v·w = 0 (with v, w nonzero), the vectors are:
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Find v×w for v = (2, 1, 3) and w = (1, 4, 2).
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If v×w = 0 for two non-zero vectors, then v and w are:
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Two vectors are v = (4, 0, 3) and w = (0, 5, 0). Find the area of the parallelogram they span.
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Triangle PQR has P(0, 0, 0), Q(2, 1, 2) and R(1, 3, 0).
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|v×w| is largest when the angle between v and w is:
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Two vectors satisfy |v| = 4, |w| = 7 and v·w = −14. Find the angle between them, to the nearest degree, and state whether it is acute or obtuse.
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Vectors a and b have a·b = 12, |a| = 4, |b| = 3. The angle between them is:
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Vectors p = (2, −1, 3) and q = (k, 4, 1) are perpendicular. Find k.
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The directions of two flight paths are u = (4, 0, 3) and v = (1, 2, 2). Find the angle between them, to the nearest degree.
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To find the interior angle at vertex P of triangle PQR using the dot product, you use the vectors:
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A triangle has vertices A(2, 0, 1), B(4, 1, 1) and C(3, 3, 2). Find its area.
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A parallelogram has two edges p = (3, 0, 1) and q = (1, 5, 2) (metres) from one corner. Find its area.
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