Practice Vector Form (8.2) - Three Dimensional Geometry

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10 questions

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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Write the vector form of a line passing through the point (3, 2, 5) with a direction vector (1, 1, 1).
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Use the formula **r** = **a** + λ**b**.
Question 2.
What is the position vector of the point (4, -2, 6)?
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Identify the coordinates as components of the position vector.
3Question 3.
What does the vector form of a line represent in 3D space?
- Position only
- Direction only
- Both position and direction
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Think about what information is needed to define a line in space.
4Question 4.
True or False: The direction vector can only change the length of the line.
- True
- False
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Recall the role of direction vectors in geometry.
Question 5.
Derive the symmetric form of a line given in vector form r = (2, 3, 4) + λ(1, -1, 2).
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Isolate λ in each component of the vector form.
Question 6.
Prove whether the lines r1 = (1, 1, 1) + λ(2, 2, 2) and r2 = (3, 3, 3) + μ(4, 4, 4) intersect or are parallel.
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Consider the relationship between direction and parallel lines.

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