Practice question · Select all that apply
Select every point that lies on the line given by r = (1, 0, 2) + t(2, 1, -1).
Hints
- Solve for t using one coordinate, then check that the SAME t works for the others.
- Try t = 1, t = -1 and t = 2.
Show the answer
- A. (5, 2, 0)
- B. (3, 1, 1)
- C. (-1, -1, 3)
Why
t = 1 gives (3, 1, 1), t = -1 gives (-1, -1, 3) and t = 2 gives (5, 2, 0). For (1, 1, 2) the first coordinate forces t = 0, which then demands y = 0, not 1. For the origin the first coordinate needs t = -0.5, which gives y = -0.5. One consistent t must serve every coordinate at once.
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