What is the vector equation of the line passing through points A(1, 2, -1) and B(3, 0, 4)?
Answer and explanation
Correct answer: A. r = (1, 2, -1) + t*(2, -2, 5)
- Step 1: Find the direction vector v = B - A = (3 - 1, 0 - 2, 4 - (-1)) = (2, -2, 5).
- Step 2: Use point A as the base point: r = A + tv = (1, 2, -1) + t(2, -2, 5).
Answer
r = (1, 2, -1) + t*(2, -2, 5).
Why not the others: using (3, 0, 4) as direction vector confuses the position vector of B with the displacement vector; using (1, 2, -1) as direction vector fails to point from A to B; using (2, -2, 5) as the base point places the line origin away from A.
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