Practice Flashcards
Flip to reveal answersHow do you find where a line meets a plane?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All 8 Flashcards — Where a line meets a plane
Sign up free to track progress and get spaced-repetition review schedules.
Question
How do you find where a line meets a plane?
Answer
Write the line's x, y, z in terms of λ, substitute into the plane's Cartesian equation, solve the resulting equation for λ, then put λ back into the line for the point.
Question
After substituting, you solve for λ in which equation?
Answer
The plane's equation becomes one equation in λ; solve that.
Question
Do you put λ back into the line or the plane to get the point?
Answer
Back into the LINE — that gives the (x, y, z) coordinates of the intersection.
Question
What does it mean if substitution gives a false statement like 2 = 5?
Answer
The line is parallel to the plane and never meets it (no intersection).
Question
What does it mean if substitution gives 0 = 0 (always true)?
Answer
Every λ works, so the line lies entirely in the plane.
Question
When are the λ-terms guaranteed to cancel after substituting?
Answer
When the line's direction d is perpendicular to the plane's normal n, i.e. d·n = 0 (the line skims the plane).
Question
Line r = (1,0,2)+λ(2,1,−1) and plane x+2y+z=9 — find the point.
Answer
x=1+2λ, y=λ, z=2−λ ⇒ (1+2λ)+2λ+(2−λ)=9 ⇒ 3λ+3=9 ⇒ λ=2 ⇒ (5, 2, 0).
Question
If d·n = 0 but a point of the line does NOT satisfy the plane, the line is…
Answer
Parallel to the plane and outside it (misses it). If a point DID satisfy it, the line would lie in the plane.
Read the notes
Full study notes for Where a line meets a plane
Topic 3.18 hub
Lines & planes (HL only)
More from Topic 3.18
All flashcards in this topic
Math AA exam skills
Paper structures & tips
Track your progress with spaced repetition
Sign up free — Aimnova tells you exactly which cards to review and when, so you remember everything before your IB exam.
Start Free