Practice question · Match the pairs
Match each geometric question about lines and planes to the algebraic test that answers it.
- Are two planes parallel?
- Is a line parallel to a plane?
- Are two lines perpendicular?
- Distance from a point to a plane?
- Project the offset onto the unit normal
- Are their normal vectors proportional?
- Is direction · direction = 0?
- Is direction · normal = 0?
Hints
- Every plane question routes through its normal; every line question through its direction vector.
- Distances are projections: how much of the offset points straight at the plane?
Show the answer
- Are two planes parallel? → Are their normal vectors proportional?
- Is a line parallel to a plane? → Is direction · normal = 0?
- Are two lines perpendicular? → Is direction · direction = 0?
- Distance from a point to a plane? → Project the offset onto the unit normal
Why
Analytic geometry is a dictionary: parallel ↔ proportional vectors, perpendicular ↔ zero dot product, distance ↔ projection. Fluency means hearing the geometric question and reaching for its algebraic translation without pausing.
Practise Lines, Planes, and Geometric Transformations
The app has 7 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
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