Unit 3: Geometry and Trigonometry
Topic 3.14: Vector lines (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.14. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
A point is on a line if, when you equate it to r = a + λd, you find:
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A line passes through C(−2, 5) and has gradient (2D direction) (3, −1). Write a vector equation and hence the parametric equations.
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For r = (0, 4, −2) + λ(3, −1, 2), find the coordinates of the point when λ = −1.
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2026
Write down the direction vector of this line.
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2026
For r = (3, 0, 1) + λ(1, 2, −1), the point at λ = 2 is:
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A line passes through P(3, −1, 2) and is parallel to d = (1, 4, −2). Write a vector equation of the line.
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A line has vector equation r = (2, 0, −5) + λ(1, −3, 2). Write its parametric equations.
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The point given by λ = 0 in r = a + λd is:
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In the motion model r = a + t·d, the vector d represents the object's:
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A line through A and B can be written r = a + λ(b − a). At λ = 1 you are at:
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Two lines have directions (1, 2, 2) and (3, 6, 6). Their directions are:
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From r = (1, 4, −2) + λ(0, 2, 1), the y-coordinate is:
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A particle moves with position (m) r = (1, −2, 5) + t(2, 1, −2) at time t seconds. Find its speed.
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A line r = (−1, 2, 4) + λ(2, −1, −2) meets the xy-plane (z = 0). Find the crossing point.
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Find a vector equation of the line through A(1, 2, −3) and B(4, 0, 1).
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A line has equation r = (2, −1, 3) + λ(1, 2, −1). Determine whether the point P(5, 5, 0) lies on the line.
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A 2D line is r = (8, −3) + λ(−2, 1). Find where it meets the y-axis.
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