Unit 3: Geometry and Trigonometry
Topic 3.15: Classifying lines (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.15. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
The denominator of cos θ = |d₁·d₂| / (?) is:
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2026
After equating components you get three equations in s and t. To find the intersection you should:
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2026
Non-parallel lines whose equations have no common solution are:
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Two lines have directions (1, 2, 3) and (2, 4, 6). They are:
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Directions (1, 1, 0) and (1, 0, 0) make an angle of:
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2026
Lines L₁ = (0, 0, 1) + s(1, 1, 2) and L₂ = (0, 2, 1) + t(1, 0, 2). Show that they intersect and find the point of intersection.
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2026
Lines r = (1,0,0) + s(1,0,0) and r = (0,0,1) + t(0,1,0) are:
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Determine whether the lines L₁ = (2, 1, 0) + s(1, 2, −1) and L₂ = (3, 1, 4) + t(2, 4, −2) are parallel.
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Show that the lines with direction vectors (4, 1, −2) and (1, 2, 3) are perpendicular.
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2026
Lines L₁ = (2, 1, 0) + s(1, 0, 1) and L₂ = (0, 3, 5) + t(1, 1, 0). Find the acute angle between L₁ and L₂.
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Find the value of k for which the lines with directions (2, k, −1) and (3, 1, 1) are perpendicular.
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Two paths are modelled by lines with directions (3, 4, 0) and (0, 4, 3). Find the acute angle between the paths, to the nearest degree.
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2026
Lines L₁ = (1, 1, 1) + s(2, −2, 1) and L₂ = (0, 5, 2) + t(2, 1, −2). Find the angle between L₁ and L₂, to the nearest degree.
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Unlock Question15Show that3 marks
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Show that the angle between the lines is .
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Unlock Question16Show that4 marks
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Show that the lines are parallel and distinct.
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2026
Which is true of skew lines but NOT of parallel lines?
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Doubling a line's direction vector changes the angle between the lines by:
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Why use |d₁·d₂| (with bars) rather than d₁·d₂?
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2026
Find the acute angle between the lines with direction vectors d₁ = (1, 2, 2) and d₂ = (2, 3, 6).
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