IB Maths AA HL Ahl 3 14 Hl Vector Equations of Lines Questions

Practise forming vector, parametric and Cartesian equations of lines, then using direction vectors for angles, parallelism, intersections and constrained motion.

Exam points

Write and interpret vector, parametric and Cartesian equations of lines in two or three dimensions, identifying a point and direction vector.
Find the angle between lines from their direction vectors and interpret the line parameter as time in a simple kinematics model.

[Maximum number: 2]

Consider the points A(1,2,3), B(k,-2,1) and C(5,0,2), where $k \in \mathbb{R}$ .

For k=9, let $L_{1}$ be the line passing through A, B and C .

Find a vector equation of the line $L_{1}$ .

attempt to set up a vector equation using a point, a parameter and a direction vector

r=\left(\begin{array}{l} 1 \\ 2 \\ 3 \end{array}\right)+\lambda\left(\begin{array}{c} 4 \\ -2 \\ -1 \end{array}\right) \text { (or equivalent) }

Note: " r= " or equivalent must be seen for A1.

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IB Maths AA HL Ahl 3 14 Hl Vector Equations of Lines Questions question 1