Practice Flashcards
What does the vector equation of a line r = a + λd mean?
Track your progress — Sign up free to save your progress and get smart review reminders based on spaced repetition.
All Flashcards in Topic 3.11
Below are all 8 flashcards for this topic. Sign up free to track your progress and get personalized review schedules.
3.11.18 cards
What does the vector equation of a line r = a + λd mean?
a is the position vector of a point ON the line, d is the direction the line points, and λ is a number that slides you along it (λ = 0 gives a, λ = 1 gives a + d).
In r = a + λd, which part is the direction and which is a point on the line?
d (the vector multiplied by λ) is the direction; a (the constant part) is a point on the line.
How do you find the direction vector of a line through points A and B?
d = B − A (finish minus start). Any scalar multiple of it is also a valid direction.
Write the vector equation of the line through points A and B.
r = A + λ(B − A) — start at A, walk in the direction B − A.
How do you find an object's position at a given value of λ?
Substitute that number for λ and add component by component: r = a + λd.
How do you test whether a point P lies on the line r = a + λd?
Set a + λd = P, solve ONE component for λ, then check the SAME λ works in every other component. One λ fits all → on the line; otherwise → off it.
Does a vector line have only one possible equation?
No — different start points a (any point on the line) and any scalar multiple of d describe the same line.
Where on the line is the midpoint of A and B, in terms of λ?
At λ = ½ in r = A + λ(B − A): a half-step of the direction from A.
Topic 3.11 study notes
Full notes & explanations for Vector equation of a line (HL only)
Math AI exam skills
Paper structures, command terms & tips
Want smart review reminders?
Sign up free to track your progress. Our spaced repetition algorithm will tell you exactly which cards to review and when.
Start Free