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4 cards from this section. Quick, good the night before a test.
Write the vector equation of a line passing through the point (3, 2, 1) with direction vector (2, 1, 0).
Use the provided point as your position vector and the direction vector directly.
What does the scalar 'λ' represent in the vector equation of a line?
Think about how you can move away from the position vector.
What does the vector form of a line in 3D express?
Think about how the variable changes the positioning.
In the vector equation r⃗ = a⃗ + λb⃗, which vector represents the starting point?
Recall which part serves as the reference point.
Two points A(1, 2, 3) and B(4, 5, 6) define a line. Write the vector form, parametric, and symmetric forms of the line.
Calculate the direction vector and begin forming representations.
For the line defined by r⃗ = (2, 3, 4) + λ(1, -1, 0). If λ = 3, find the coordinates of the corresponding point on the line.
Substitute λ into the parametric equations derived from the vector form.
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