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Flip to reveal answersHow do you test whether a point lies on a line r = a + λd?
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All 8 Flashcards — Points on a line
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Question
How do you test whether a point lies on a line r = a + λd?
Answer
Solve for λ from one coordinate, then check the SAME λ satisfies every other coordinate. All must agree.
Question
How do you find the point on a line for a given λ?
Answer
Substitute that value of λ into r = a + λd and compute each coordinate.
Question
Where does a line cross the x-axis (in 2D)?
Answer
Where y = 0: set the y-equation to 0, solve for λ, then substitute back for x.
Question
In 3D, a point is on the z-axis when…
Answer
x = 0 AND y = 0 (only the z-coordinate is free).
Question
In the motion model r = a + t·d, what is the speed?
Answer
Speed = |d|, the magnitude of the velocity (direction) vector.
Question
Speed of an object with velocity (4, 0, −3)?
Answer
√(4² + 0² + (−3)²) = √25 = 5.
Question
What does the parameter t mean in a motion model r = a + t·d?
Answer
t is the time; a is the start position (t = 0) and d is the constant velocity.
Question
If a point gives different λ values in different rows, is it on the line?
Answer
No — the point is off the line; one λ must satisfy all coordinates simultaneously.
Read the notes
Full study notes for Points on a line
Topic 3.14 hub
Vector lines (HL only)
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Math AA exam skills
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