Unit 3: Geometry and Trigonometry
Topic 3.18: Lines & planes (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 3.18. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
A line and a plane in 3D, in general position, intersect in:
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2026
To get the intersection POINT after finding λ = 3, you substitute λ = 3 into:
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2026
The angle between two planes equals the angle between:
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2026
Find the coordinates of the point on the line when .
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If a line's direction d satisfies d·n = 0 (n is the plane's normal), the line is:
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2026
For r = (0,0,0) + λ(1,1,1) and plane x + y + z = 6, the parameter at the intersection is:
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The line r = (2, 1, 0) + λ(1, −1, 2) meets the plane 2x + y − z = 5 at a point P. Find the coordinates of P.
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Find the acute angle between the planes Π₁: 2x − y + 2z = 5 and Π₂: x + 2y + 2z = 3, giving your answer to one decimal place.
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2026
Planes with normals n₁ = (1, 0, 0) and n₂ = (0, 1, 0) meet at an angle of:
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For the angle between a line and a plane you should use:
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To get a POINT on the line where two planes meet, a quick method is to:
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Substituting a line into a plane leaves '5 = 5'. The line:
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2026
Find the exact value of cos θ for the acute angle between the planes x + y = 2 and y + z = 5.
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The line r = (4, 0, −2) + λ(−1, 3, 1) crosses the plane 3x + y + 2z = 6 at point Q. Find Q.
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Show that the line is parallel to the plane.
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Show that these planes are parallel and never meet.
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Find the angle between the planes.
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Find the coordinates of the point where the line meets the plane.
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Find a vector equation of their line of intersection.
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