5.1 - Vector Form
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Practice Questions
Test your understanding with targeted questions
Write the vector equation of a line passing through the point (3, 2, 1) with direction vector (2, 1, 0).
💡 Hint: 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?
💡 Hint: Think about how you can move away from the position vector.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the vector form of a line in 3D express?
💡 Hint: Think about how the variable changes the positioning.
In the vector equation r⃗ = a⃗ + λb⃗, which vector represents the starting point?
💡 Hint: Recall which part serves as the reference point.
1 more question available
Challenge Problems
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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.
💡 Hint: 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.
💡 Hint: Substitute λ into the parametric equations derived from the vector form.
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